Short answer

Pro:

Nationalism started in Prussia during the occupation of Napoleon where the lower, middle and higher classes, for the first time, banded together in opposition to the French occupation.

This resulted in a feeling of belonging to something, instead of just being a part of something.

So peaple in these area consider themselfs to be Prussions and not just subjects of the Prussian King.

Contra:

In other areas later, peaple became Prussian soly through the decisions of others who didn't care who the effected peaple felt about it.

Rheinland is a prime example of this.

One result of the French Revolution was that France's borders were expanded to France's natural borders. As in today's area of Belgien, the initial joy of the fruits of the Revolution were short lived.

In the long term, however, the economic advantages resulted in that most peaple became very confortable the situation.

One result if the Vienna Congress of 1814/15 was that Rheinland became a Provence of Prussia.

The Rheinlanders resented the fact that the Austrians, British, Royal France, Prussia and Russia simply carved up a map as it please them without considering the effects of the peaple involved .

This attitude is reflected in the supposed quote in the 1920's from Konrad Adenauer:

bei Braunschweig beginne für ihn die asiatische Steppe

The Asian steppe starts after Braunschweig

Answer in conjunction with backround information explaining why many felt the way they did

The German Empire was a federation (Bund) of Kingdoms, Duchies, City States etc.

• Prussia and Bavaria were 2 of these Kingdoms
  • each being a member of the Bundesrat (Upper House, Senat)

Prussia was subdivided into Provences

• Brandenburg, Pommern, Schlesien, East-Preußen and West-Prussia

Each Kingdom had it own Parliament and Prime Minister who was the representative in the Bundesrat.

Until 1919 you were a citizen of the Kingdom with German nationalty and was so stated in issued Passports. wiki auf Deutsch

In 1919 the Kingdoms became states of which you were a citizen of with German nationalty. wiki in English

1934 the single citizenship was introduced.

So these Kingdoms, including their subdivisions, have existed for centuries with different

• customs, dialects, food and of course beer

An extra Parlament existed for the Reich (Abbreviation for Deutsches Reich) and was called Reichstag (Lower House).

How the Kingdoms envolved is just as diverse as the amount of them

• wars (internal and external), marriages being the major causes

and are often the cause of differences inside each Kingdom

• Franken (North Bavaria) are completely different than Ober-Bayern (South Bavaria), with a different religion, dialect, food and beer
• Rheinland became a Provence of Prussia as a result of the Vienna Congress after the fall of Napoleon
  • they resented that the Austrians, British, Royal France, Prussia and Russia didn't asked them if that was what they wanted
  • they had been living under the results of the French revolution and had gotten used to it (more or less)

Nationalism started in Prussia during the occupation of Napoleon where the lower, middle and higher classes, for the first time, banded together in opposition to the French occupation

• this was when they stared to consider themselfs to be Prussions and not just subjects of the Prussian King

It also helped that before the French Revolution

• serfdom had been abolished (1763)
• introduction of mandatory education for children (1717/1763) (wiki in German)
• PrALG 1794 (German) law codex (English) , replacing justice based on the wim of an aristocrats and/or lawyers
  • 'must be written in a form that everybody can understand'
• 1740, 1812 religious freedom for Catholics and Judaism (1740 only partial, 1812 full) (wiki in German) in a Protestant country, when elsewhere in Europe discrimination among Christians was ramped and Gettos commonplace

as the first in Europe and was, compared to other contenental European countries very tolerant.

Prussian law was the base of German law, but the final result was the merging of the Napoleon law books (still used in the Rheinland and Southern Germany) taking the best of both.

By 1901 (compleation of final lawbooks)
(only German wiki pages exist for these topics)

• initial development of healthcare systems (1845, 1867, 1873)
• mandatory heathcare for all (1883)
• the present day pension system existed (1889)

So in 1919 (Weimar-Constitution) a very sound foundation existed to build apon.

The result, at this point of time, was a unified society that respected the diversity of the regions.

A major social problem, as a result of the Industrial Revolution, was inadequate housing conditions for workers in major cities.

This came to an abrupt end with National Socialism.

They extracted only those portions of Prussion society that served their purpose and reverted the rest

• diversity, tolerance and the reintroduction of serfdom

Just as Frankenstein created his monster, so did both the National Socialist and the Allies (in WW I and II) their monster out of the bit and pieces that served their purpose.

Many of the stereotypes created then are still believed today

• most of which you will not find in pre 1914 lituratur
  • one should wonder why

It might be helpful here to remember that the German unification was accomplished by Prussia in 1871. During the interwar period after WWI this was still in living memory.

Prior to unification, Prussia had slowly taken over nearly all of northern Germany. The rulers of the new German Nation were the same Hohenzollern family that ruled Prussia, and their chief advisers were the same kinds of folks who had avised them when it was just "Prussia" they were running.

So when talking about how things in Germany were run, for a few decades after unification it was a useful conceit to refer to this ruling class as Prussian.

Note that Bavaria is that large unconquered state in the South East. So for a Bavarian, talking about Prussians would also be a way of separating themselves from the northern Germans who were running things. I believe Bavarians like to view themselves as more laid-back than other Germans, and are mostly renowned for their food and beer.

The whole premise needs to be reversed.

The entire question is extraordinarily broad and potentially encompasses developments over 800 years and the entire globe.

What was Prussia, exactly, and what were "Prussians", and when did anyone call themselves "Prussian"? Those are the subquestions presented in the question body. But that is peripheral to explaining the quote in context. Let's address them anyway:

Quite a few non-German, non-Christian (Old-)Prussians ('Prusai or Pruzzen') gave the smallish territory on the Baltic their ethnic name. This was conquered by Teutonic Knights on a medieval crusade, came under control of different Germanic aristocrats who had to be loyal to the Polish Crown, then this duchy went to Brandenburg-based Hohenzollern dynasty. As self-identification of inhabitants of what was for a long time 'East-prussia' the word Preußen appears around 1400. They expanded their personal land-holdings and wrested away the loyalty to the Polish Crown and turned instead the Prussian territory outside of the Holy Roman Empire into a base to claim themselves King – not a 'German king' but 'King in Prussia'. Before 1701 then, absolutely no-one outside of Prussia proper would be called "Prussian".

Even in historiography it took quite a while that the Hohenzollern holdings were contracted to an anachronistic description of 'Brandenburg-Preußen' (which encompassed the main lands of the speckled colourings of the map. So the name migrated East for the polity boundaries.

For ethnic self-attribution things changed a lot slower. A Silesian stayed a Silesian under Prussian overlordship when Frederick conquered the place. This changed only a bit after nationalism took hold: Rhinelanders dissented with being annexed by Prussia, as did Northern-Saxons, but less so:

After Napoleon the polity of Prussia expanded ever more until it reached this extent:

But that still doesn't mean that everyone under Prussian control identified as Prussian. They could, that was now the state they lived in. That would be strongest among ruling elites, or in Berlin and Prussia proper ("East-Prussia") but would then decline rapidly when going anywhere else on the map or down the social strata. People had a much more local identity throughout the entire 19th century. That doesn't rule out that they also would have had multiple identities. Not only could Silesians become 'good Prussians' in terms of administration, they could also switch tribal or ethnic self-identification as needed or depending on "who asks".

This is evidenced when after founding the empire Bismarck argues about his strategy for the Berlin Balkans Conference:

"of no interest for Germany, […] which would even be worth […] the healthy bones of a single Pomeranian musketeer".

And this continued well into the World War. After Napoleon inhabitants of newly acquired Prussian territories felt either their former locality as primary or 'being German', as it was no longer fashionable to become an ethnic Prussian. Politically this was again different and the elites assimilated still longer and stronger into 'Prussians'. But for a Prussian subject of for example the Rhineland "I am with the Prussians now" would just mean "I was drafted into the army".

For the former Kingdom of Hannover – annexed in 1866 – this was called "the time when the Prussians invaded", and led to people loyal to House Hannover resenting it hard enough to support a separatist party that supported and honoured George V. to the present day.

Yet, all this is not really helpful for explaining the confusion displayed in the question.

The book in question is not about anything 19th century or prior. The question title is really broad, but body has a focus that indicates that for a precise answer: we need to pose the question differently:

have a fictional book (made for German language learners) that takes place in inter-war Bavaria, there is someplace a joke about people arriving late, and their professor answer them:

Pünktlichkeit ist eine Preußische Tradition

(German for : Arrival on time is a Prussian tradition)

This particular quote really made me scratch my head because this book was only about Bavaria, which on paper has nothing to do with Prussa, so why would the guy give a damn about so-called "Prussian tradition" ?

That's about Bavarian attitude towards others, so: "Who did the Bavarians identify as 'Prussians'? And what do they attribute to them?" That then is best captured with the maps presented so far and a few others.

Proper Bavarians are only found in the old territories of the modern federal state, as they expanded just like 'Prussia' and profited enormously from betraying Napoleon just at the right time:

More exactly tied to the book: "What did inter-war Bavarians call Prussian?"

Bavarians called 'Preißn' everything 'German' North and East of Bavaria, or in their very own words:

Breiß is a Schimpfwort, des einglich fia Norddeitsche heagnomma wead. Synonyme Schimpfwäata fia Breissn im Sinn vo Norddeitsche han no Nordliacht oda Fischkoobf. De Grundfoam Breiss ko ma ano mit andre Woerta zamdoa um de Boshaftigkeit zum vasteakn. Recht oft wean do Woerta vom Land gnumma, "Saubreiss" und "Mistbreiss" san blos a boa.

Which makes clear that this is an insult, which can also be used mildly derogatorily or jokingly.

Again the definition:

"Prussian" is:

• the name for the inhabitants of the former national territory of Prussia
• in southern German a disrespectful name for northern Germans, see Preißn

Where did and do they draw the line?

Variously, on polity boundaries, at the Main, or at the 'Weißwurstäquator':

What do the Bavarians in the book attribute with "Prussian"?

In this case one of the so-called Prussian virtues, punctuality.

These virtues, and punctuality especially coould also be called as a "German virtue". But as this is an educational book it also alludes to this virtue as a secondary one:

Among the bourgeois or secondary virtues were especially diligence, loyalty, obedience, discipline, sense of duty, punctuality, reliability, love of order, politeness, cleanliness etc., mostly from the catalogue of Prussian virtues or the "bourgeois" catalogue of virtues. In 1963 Otto Friedrich Bollnow once again confirmed order and cleanliness, diligence and truthfulness, but already registered "the declining understanding" in society.

This of course leaves out the 'absolute obedience to military commanders and their orders' as one of these secondary virtues. The virtues stand in a contrast of emphasis with cardinal virtues and the post Second World War public debate partly identified this imbalance between primary and secondary virtues as one of the reasons for why Prussian militarism was one cause for both World Wars. And the allusion in the book further paints a difference in perception between very sticklish Protestant Northerners and slightly more relaxed, Catholic South-Germans. Bavarians liked to point out that the balance between cardinal and secondary virtues was much more upheld there, even if that difference wasn't really there.

Prussia no longer exists in any form. Bavarians still tend to call people from Hamburg "a Prussian" (if not 'fish head' or other derogatory stuff), despite Hamburg Never being subject to Prussian rule. And the Bavarians aren't really known for being late on time. Although, the confusion causing quote might as well be read as the corollary to "the Prussians do not shoot that fast".

"Prussia" is an area on the East Baltic, conquered by the Teutonic knights, who assimilated the local "Prussian" people. In part because they were on the frontier between Germany and Slavic lands, they became a particularly militaristic group. Imagine if American soldiers in Iraq annexed the country and intermarried with the locals to create a mllitaristic breed of American "Iraqicans" through natural selection.

Prussia merged with Brandenburg in the modern East Germany in the 16th century when the Duchess of Prussia married the Elector of Brandenburg. Because of this fact, Brandenburghers often considered themselves "Prussian" even though technically they are not.

The combined entity then acquired many other lands, some to the west, as far as the Rhineland, and some in the intervening area between Brandenburg and Prussia. On the whole, the western, Rhinelanders tended not to consider themselves "Prussian," while the eastern people (between Germany and Poland) often did. Basically the closer you got to the original Prussia, the more likely people were to think of themselves as "Prussian." Most Germans identify themselves as "Prussian" or NOT. Which is why this might matter to a "Bavarian."

Some people consider themselves "Prussian" even today, especially people who were refugees from (East) Prussia after World War II. I once dated a woman whose mother is American and whose father was "Prussian" who considers herself "Prussian."