Possession after a double tech?

[M&M Guy]

Originally Posted by bas2456

Team A was about inbound on the baseline when the horn sounds. Our scorekeeper informs me that one player from each team hasn't signed in (ie not listed in scorebook) and both players had entered the game. I called my partner over and we quickly agreed that a double administrative tech should be issued. I called the captains over and explained what was happening. We shot two free throws for each side, and then we were about to give the ball to Team A at POI, but my supervisor came over and was very adamant that after a double tech, we use the AP arrow.

What's correct and/or incorrect about this situation?

EDIT: Sorry, NFHS rules.

Tell your supervisor to read a copy of the rules. 4-36-1 is the definition of Point of Interruption, which is the method of putting the ball in play after a double technical.