TMP/TWOK established TOS as in the 23rd Century, but there were some offhand remarks in some TOS episodes that implied it's just "a couple of centuries" from now, so the early 23rd-Century was accepted by many fans and even some tie-in works back in the day (pre-TNG).
Actually, the banner in TWOK only said "In the 23rd-Century..."
IIRC, Decker's line in TMP didn't really move the needle that much. Some took Decker as speaking figuratively and still kept TOS (and TMP) in the early 23rd-Century. Both the FASA games and the often lauded Mr. Scott's Guide to the Enterprise reference book did the same, even placing the launch of the Enterprise-A in TVH in the year 2222.
And then there was Data's infamous line in "Encounter At Farpoint" about graduating from the Starfleet Academy "Class of 78," which many took as "the Class of 2278," which they thought supported the idea of TOS taking place much earlier.
Then Data (again!) informed everyone that the year was 2364 in "The Neutral Zone" and that definitively ended the idea that TOS took place in the early 23rd-Century once and for all.