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NFHS
I can't speak for the NCAA, but I wouldn't expect it to be different.
The point is that if a period has ended and there will be a next period, then any T during the intermission (even if only 1 minute long) is part of the next period. The break belongs to the following period.
However, if there is not another period planned (i.e., game is over if nothing happens), then any such action is considered part of the previous period. So, A=56 B=57 after 4th and coach B reveals his/her true feelings: T and, since there is no planned additional period, team A shoots 2 shots as part of 4th period. If both are made, you expect the final to be A=58 B=57. If only 1 shot is made, then the score is A=57 B=57 and you will play an overtime period, initiated with a jump at center court. (The T and its associate activity belong to the 4th period because you did not expect to play another period.)
Hope that helps.
Now here's my twist and question: In above scenario only 1 shot was made, so the score is A=57 B=57. As we get ready for the overtime period another T is assessed. (Oh my!) Are we still in the 4th period? or once we determined that an overtime period would be played, are we now in it. IOW, will the overtime now start with 2 freethrows instead of the jump? (I wish I didn't think of these complications.)
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