It seems that you answered your own question. The responsibility to rule a shot as either a 2 point try or a 3 point try rests on the floor officials.
Now, if it is a question of the floor officials not seeing/hearing the end of period signal, it is permissible for the R to get additional info from the timer, to then determine if a shot was away before the end of the period. Even in that case, the final decision is up to the R. That circumstance is covered in 2-13, and Case Book 2.13.
Live and learn.
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To be good at a sport, one must be smart enough to play the game -- and dumb enough to think that it's important . . .
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