Administrative T's quarters apart

[Amesman]

Fellow ref wondering if he kicked the handling of some administrative T's recently so I told him I'd ask.

The scenario (fed rules): Team A makes a change to a player number less than 10 minutes before the game. Team B takes two FTAs and the ball at the division line to start the game.

Then, sometime in the third quarter A6 enters the game and the scorekeeper notifies the crew that he's not in the book at all.

The crew whistles another technical, shoots 2 FTAs and gives the ball to Team B at the division line. That night, my friend checks 10-1 and hits self in the forehead. One foul "regardless of the number of infractions" never hit their radar in this context. I have to admit that it didn't hit me either when he told the story the next day -- it seems that this is always on the annual test, but usually posed so all the infractions are happening before the game starts.

So, two questions: 1) Did they kick it by calling another T, awarding free throws and then giving B the ball? 2) If so, does that mean the game merely stops when the infraction is caught and ... no foul is added to the team total, no free throws are awarded and the ball isn't automatically given to the non-offending team?

Sounds odd and the casebook isn't any help.