Jump ball to start the game.... After the ball is tossed, B1 violates. When is the possession arrow set?
6.3.1 When the ball is in the possession of the thrower of Team A, the arrow is "immediately" pointed in the direction of B's basket.

My question is.... What makes this a special case?
Just because "B" violates doesn't give "A" team control. Giving the thrower from team "A" the ball doesn't give "A" team control.
Normally the arrow isn't switched until the end of the throw-in. Even in this case setting the arrowing after the throw-in has ended seems to work ok.
So, What's the hurry in this case?

When A is handed the ball for the throw-in, team A has team control (at least as defined for the AP rules).

If you waited until after the throw-in, then A1 could throw to B2, team B would have control, and the arrow would go to A.