At the jump ball to start the game, A1 and B1 each tap the ball. A1 then catches the ball before it hits the floor or touches a non-jumper. We called the violation, but the question came up as to who now gets the AP arrow. We set it towards B with this rationale: A obtained possession of the ball first. It then led to the violation. So B got the ball OB at the violation and it also got the first AP arrow. Any help?

In Fed rules, you would be exactly right.

In NCAA rules, the arrow is set the other way. The rationale is that the first LEGAL possession is by B, so you would set the arrow to A after the throw-in is complete. There's an Approved Ruling about this, but I'm too lazy to look it up. :)

B gets ball and arrow - make sure that the table doesn't switch it back to A after B's initial throw-in!