Weird T Situation

[fiasco]

B1 fouls A1 during a shot attempt as time expires to end the third quarter. None of the officials have certain knowledge of any time that should be left on the clock. Immediately after the official whistles the foul, A2 commits an intentional technical foul on B2. The arrow is pointing to A's basket.

I need to understand a few things. Am I right in saying that the technical foul occurred in the third quarter? Because A1's free throws should be a part of the 3rd quarter, and they haven't occurred yet?

So, we have a false double foul. A1 shoots two free throws, followed by 2 free throws by a B player.

My question is now how is the second part of the penalty administered? Since the T occurred in the third quarter, does the second part of the penalty (ball out of bounds at the division line opposite the table) carry over into the fourth quarter? If so, what is the rule justification?

TIA...