Jump ball to start overtime period. Player A1 tips the ball and then catches it himself, before it touches another player or the ground. Clearly a violation and ball is given to team B. Which was does the possession arrow now point?

Team B will have the arrow for the first alternating-possession throw-in since A1 had control when he caught the ball.

KDM

In NF rules, Team B gets both the arrow and the ball since A1's catching the ball counts as control for establishing the arrow. Case 6.3.1C(d).

I had never had this call before, yet i've had it 5(!) times this season already. Believe it or not, a couple of the coaches didn't believe me when i explained that the other team got both the arrow and the ball...

BTW, my understanding is that under NCAA rules, the offending team would get the arrow...

This situation is very similar to having a throw in violation on an alternating possession throw in. For instance, after a jump ball, b1 attempts a throw in but crosses the line. A1 gets the ball AND the arrow being that the ball was at the disposal of b1 at the time of the violation. A VERY hard sell to a coach that doesn't know the rules!!

Jeremy is exactly right!

Also remember on a Alternating Possession throw-in if Team A player A1 is making the throw-in and A2 fouls B1 during the throw-in but before it ends then Team A does not lose it's arrow. Team A would have the next AP throw-in.
Under the AP throw-in procedures Violations are different than Fouls.