Did USS Buck (DD-761) send the message “Temper, Temper”?

tl; dr

There is some evidence to show that the message was, in fact, sent during that engagement, but it seems unlikely that it was the USS Buck that sent it. It seems more likely to have been the USS Duncan (DDR-874).

Eyewitness account

There is a Facebook group dedicated to the USS Wisconsin (BB-64). This picture of the damage sustained by USS Wisconsin on 15 March 1952 was posted there on the anniversary this year (15 March 2019):

A member of the group, whose father served on the USS Wisconsin at the time posted the following:

"My dad told me about this. If I remember the story correctly this is when the USS Wisconsin received the message, “Temper, temper”"

Which is anecdotal evidence from an eyewitness (albeit at second-hand), which does suggest that the story of the message from an escort vessel may be true.

The Daybook

The Daybook is an authorised publication of the Hampton Roads Naval Museum which currently manages the battleship USS Wisconsin. In Volume 7, No 4 they relate two stories about the incident.

The first of these, part of the article titled 'Freedom Fighter: Battleship Wisconsin in the Korean War', states (on page 16):

"After observing Wisconsin returning the North Korean challenge in dramatic fashion, Duncan signaled to the battleship “Temper, Temper Wisconsin.”

This being a reference to the destroyer USS Duncan (DDR-874), the article having previously noted (on page 14):

"In early March 1952, Wisconsin and the destroyer USS Duncan (DDR-874) steamed north as part of an overall effort by the Navy and Air Force to strike targets deep inside North Korea ..."

Unfortunately, since they do not explicitly state their sources for the article, this cannot be considered canonical. However, as their website notes, the Hampton Roads Naval Museum Library "collects materials associated with the battleship Wisconsin", so it seems likely that the story has some evidential basis (which may, of course, be the recollections of men who served on her during the Korean War).

The second reference (on page 12), challenges the claim on many sites on the Internet (although no on the Reddit thread you cited) that the USS Wisconsin was hit by a 155mm shell. They point out that:

"the North Koreans didn’t use the 155-mm howitzer, as it is an American caliber"

and that

"It is a known fact the Soviets handed over a number of 152-mm guns to their North Korean allies."

It is interesting to note that, while I've found while trying to track down the source of this story, most of the sites that state the message was from USS Buck also state that the USS Wisconsin was hit by a 155mm shell.

Naval History and Heritage Command

This identification of the escort as the USS Duncan seems to be confirmed by the website of the Naval History and Heritage Command, on its Korean War: Chronology of U.S. Pacific Fleet Operations, January–April 1952 page, which notes that on 16 March 1952:

"USS Wisconsin (BB 64) and USS Duncan (DDR 874) at Songjin Chaho area; received four salvos from shore battery vicinity Dojo-ri. One direct hit slightly injured three personnel, material damage to Wisconsin negligible. Wisconsin scored 2 direct hits in counter-fire."

After Action Reports

Unfortunately, although some After Action Reports from the Korean War are available online (including a collection available to view and download from archive.org), the actual After Action Report covering this incident doesn't appear to be among them (yet).

This may well be part of the collection 'Reports and Other Records Relating to Korean War Military Operations, 1950 - 1956' held by the US National Archives. This collection is described as follows:

"This series consists of reports and other records relating to U.S. Navy and Marine Corps operations during the Korean War. Included are final reports on U.S. Pacific Fleet operations, and on the First Marine Division operation at Chosin Reservoir. After action reports on other operations, and many maps and map overlays are included. There are national intelligence surveys on Korea, and transcripts of interviews with Marine officers about their combat experiences. Illustrated pamphlets on major lessons of the Korean War, and published historical studies on U.S. Air Force operations in the war are also included. At the end of the series is an Army War College conference report on United Nations military operations in Korea to the end of 1951, and First Marine Division general orders designating combat units in Korea for 1953. The records were maintained by the History and Museums Division and its predecessor."

Since the Hampton Roads Naval Museum also maintains an extensive collection of material relating to the USS Wisconsin (as it says on their website), they may well also have copies of the reports there (in addition to records of the recollections of men who served on her during the Korean War).