Rule 5 - 2010-2011 Case Book Page 42
5.6 Comment B: "If a technical foul occurs after the ball has become dead to end a quarter, the next quarter is started by administering the free throws. This applies even when the foul occurs after the first half has ended. It also applies when the foul occurs after the second half has ended, provided the score is tied. If the score is NOT tied, the free throws ARE administered unless the outcome of the game will NOT be affected. If the outcome is not already decided, the free throws are attempted immediately as if the foul had been part of the fourth quarter. The division line throw-in following the technical foul cannot be carried over to the overtime as the fourth quarter ended with the last free throw." See Rule (5-6-4)
That rule reads "If a technical foul occurs after the ball has become dead to end a quarter or extra period, the next quarter or extra period is started by administering the free throws. This applies when the foul occurs after any quarter has ended, including the FOURTH quarter, provided there is to be an extra period. If there is no way to determine whether there will be an extra period until the free throws are administered, the free throws are attempted immediately, as if the foul had been a part of the preceding quarter."
So, if the score was tied and the fourth quarter had ended, (as per your initial post) and the technical then occurred with the score tied, the officials erred in their decision. The shots should have been taken to start the overtime, and the shooting team should get possession opposite table to start the overtime period. I have been a high school official for ten years, and always find unique rulings interesting. I hope this shines some light on the situation.