I've read Rule 4-13, 4-35 and still don't know what the proper call should be? Ball brought in on the side, close to half court line. Offensive player is coming back to the ball hard with defensive player on his hip. Lobb pass is thrown as the players reach half court line. Both player leap for the ball. Offensive player in the front court jumps and tips the ball while in the air. Then lands in the back court. Both players sprint for the ball, offensive player gains control.
Coach is screaming for a back court call. Since the player never had control in the front court, never had both feet and the ball, I did not call back court. What is the correct call?

You are correct.

The tip is not control, therefore no violation.

Even if the offensive player was in the frontcourt (with both feet on the court) and the TI was tipped by him into the backcourt, he could still revover (first to touch) the ball in the backcourt. In your scenario there is no team control on the TI, nor on the tip by the offense, regardless of position.

Team control first exists upon recovery by the offense in the backcourt.

Thank you. I thought I was correct but this school and coach are supposively well educated in the game. I was afraid I interpreted the rule incorrectly.

Having both feet and the ball in the FC is only an issue when the player is dribbling from the BC into the FC.

Your player had FC status. But there's no team control. Further, the rule allows him to leap from the FC, catch the ball, and land in the BC on a throw-in.

Well educated by coaching standards. This means that in comparison to the rules knowledge referees have, they would get an F- if graded on the curve.