A1 has control in the frountcourt throws a pass which is tipped by B1. The ball is traveling back towards the ten second line before the ball crosses the 10 second line A1 tips the ball again and A2 recovers the ball in the backcourt. My guess is that it is a violation because team A never gave up possesion to team B so technically they still had possesion. Am I right

Yup!

It's a violation because A had team control in their front court, A was the last to touch the ball in the front court, and A was the first to touch it in the back court. If the ball had not touched A1 after it touched B1 in the front court, there'd be no violation.

A was the first to touch the ball after it went to the backcourt. He doesn't have to touch it in the back court for it to be a violation.