Is it never what you think it is?

When I want to analyse a sutta or a translation there are two places I turn to.

One is Ven. Sujato's translation with the "View root text with translation" and "Activate Pali word lookup" options enabled.

That gives this:

The Buddha has spoken of not identifying even with the attainment of the first absorption.
‘paṭhamajjhānasamāpattiyāpi kho atammayatā vuttā bhagavatā.
For whatever they think it is, it turns out to be something else.’
Yena yena hi maññanti tato taṁ hoti aññathā’ti.

I think that's more like the first translation you quoted than the second -- i.e. it explicitly references the first jhana.

The second one you quoted gives you the impression that it might be a more general statement, presumably because it says "in whatever way they conceive" and not "whatever way they conceive it".

Ven. Sujato's translation says explicitly "it" (referring back to the previous sentence); and I think that's justified by the word tato.

I'm not denying that atammayata isn't a good thing generally, but to answer your question I think that here the object is specifically the first jhana.

But the English translation says literally, "For whatever they think [the first jhana] is" -- however perhaps a different translation might be, "For whatever opinions they form [about anything] from the first jhana" ("from" being a translation of tato), which tends again towards that second (more general) meaning.

The other place I go is Piya Tan's analysis (if there is one); partly because he references other writers, and commentary, and so on.

His analysis for MN 133 is here -- https://www.themindingcentre.org/dharmafarer/wp-content/uploads/2009/12/23.7-Sappurisa-S-m113-piya1.pdf -- (at least for the moment, the URLs on that site aren't very stable).

Spiritual practice is not based on dhyana

21a (19) CONCEIT ON ACCOUNT OF DHYANA ATTAINMENT. Furthermore, bhikshus, a false person, quite secluded from sensual pleasures, secluded from unwholesome mental states, attains and dwells in the first dhyana, accompanied by initial application and sustained application, accompanied by zest and happiness, born of solitude.

66 He reflects thus: ‘I am an attainer of the first dhyana attainment, but these other monks are not attainers of the first dhyana attainment.’ So he praises himself and belittles others on account of his being an attainer of the first dhyana attainment. This, bhikshus, is the nature of a false person.

21b But a true individual, bhikshus, reflects thus: ‘The Blessed One has spoken of the non-identification with the first dhyana attainment, too. For, in whatever they conceive, it turns out to be something else.’ So, keeping at heart [keeping in mind] only the practice of non-identification with the first dhyana attainment, he neither praises himself nor belittles others.

I think that suggests that ...

• The whole sutta is is a list of various types of conceit or objects of conceit
• For each possible type conceit there's a (different) remedy or counter-acting thought, practiced by the true individual
• The remedy for being conceited about attainment of the first jhana is atammayata

... and therefore, again, this sutta mentions atammayata in the specific context of the first jhana.

The Chan/Zen tradition, for this reason, has always emphasized “special transmission outside the teachings, without reliance on words and letters.”

Case 40 in the Mumonkan (Gateless Gate) illustrates this perfectly:

When Isan Oshõ was with Hyakujõ, he was tenzo [典座 head cook] of the monastery. Hyakujõ wanted to choose a master for Mount Tai-i, so he called together all the monks and told them that anyone who could answer his question in an outstanding manner would be chosen.

Then he took a water bottle and stood it on the floor, and said, "You may not call this a water bottle. What do you call it?"

The head monk said, "It cannot be called a stump."

Hyakujõ asked Isan his opinion.

Isan tipped over the water bottle with his feet and went out.

Hyakujõ laughed and said, "The head monk loses."

And Isan was named as the founder of the new monastery.

In a more contemporary case, I've seen a Zen teacher point to a wooden arm rest and ask his Sangha: "what would you call this?" When some answered "an arm rest" he said "no it's not!", and started slapping his hands on the object, saying "now it's a drum."

It's not that what you think it is doesn't describe some of the properties of an object, it's that what you think it is or how you name it limits your perception of it.

Thanks to ChrisW for additional clarifications.

In my understanding, this is a reference to a folk poem-turned-proverb popular at Buddha's times about impermanence and the futility of human condition:

Yena yenahi maññanti,
Tatotassa hi aññathā;

In whatever way you think of it
It invariably gets otherwise.

Here Buddha creatively uses it to emphasize the point he's making about confusing any particular meditative state with Nirvana. However refined, any meditative state is fleeting, "it invariably gets otherwise". In whatever way one tries to grasp it and make it into something one can own and be proud of -- true Nirvana remains unreachable to the grasping mind. It cannot be held onto, cannot be conceptualized, it can only be realized through actually letting go, or, in Mahayana terms, through embracing Shunyata as one's actual modus operandi.

You can see on my example right here in the previous paragraph that, indeed, as soon as you use a positive statement to describe Nirvana, your very words become a conceptual box limiting the vast open space and misrepresenting the living realization.

Or to paraphrase OP's apt question title, Nirvana is never what you think it is.

To answer your question directly: the poem speaks about impermanence of everything in life in the general sense, but when the Buddha quotes it he refers specifically to the impermanence of meditative states vs the letting go of grasping at conceptual boxes (atammayata) as the only true Nirvana.