While defending A1, B1 taps the ball towards the backcourt. When A1 attempts to gain control of the tapped ball, A1 touches the ball near the center division line in the frontcourt, however, his momentum carries him into the backcourt where he secures his dribble. Is this a backcourt violation?

Yes, it is. It makes no difference whether whether the defender touches the ball or not. It's a matter of who last touches the ball before it enters the BC.

Yes backcourt, last to touch , first to touch

But when B1 tapped the ball, nobody has control, so there is not team control, for it to be a backcourt.

Just like in the inbound there is not team control and that sict can happen and is not a back court violation.

That is what I think. I migh be mistaken.

You would be mistaken. Team A, having had control prior to the tap, retains control until one of three things happen: B secures control, A shoots, the ball becomes dead.

Is it a backcourt violation taking the scenario above and putting it in a college game with team A inbounding, because there is team control on an inbounding play in college, right?

No. My understanding is that team control exists for the purpose of a team control foul but the same exceptions still exist.

Tony's correct. No surprise there.

Thanks everyone. I'm just disappointed that I got this call wrong.

I believe that this is the way the NBA does it. Team control ends on a defensive bat. College and HS do not have this rule. That is likely the source of much misunderstanding at the HS level.