tip vs controlled tap
 

A1 jumps in the air, grabs the rebound with both hands and before coming back down to the floor is fouled by B1 for a slap on the arm. Basket is good. award the basket and go to the line for 1 shot. My question is this the same for one handed tip that you do not call controlled.

Try = Tap in Your Sitch
 

Yes. Note 4-41-1, and how the words "try or tap" are used together commonly in the rulebook, especially 10-6 PENALTIES 2, 5, and 6.
Probably best not to consider a "tap" from the viewpoint of "controlled". Whether one considers it so or not is irrelevant. A tap is treated the same as a try as regards Act of Shooting which determines result of a foul.

Don't be confused by 1 hand vs 2 hand. The ball is held and in control when the ball comes to rest even in one hand. Too many people, in too many situations, think that a firm two-handed grasp of the ball is the minimum to be considered holding the ball and in control. It is not.

If they are able to control the direction of the ball such that it goes in the basket, I'd call that control, even if brief. And, even if you don't consider it "controlled", the rulebook, as noted by Freddy, effectively treats it the same. It is really, more often than not, a brief catch.

Misty Water Color Memories ...
 

Questions about such situations are probably remnants of a long ago changed rule. Back when I started officiating, about thirty-three years ago, there was a difference between a try, and a tip. Being fouled in the act of a try led to free throws. Being fouled in the act of a tip only led to free throws if the team was in the bonus.

I guess that all of us old timers are going to have to die before we put all such questions, myths, and legends, to rest.

We don't call it controlled, fans do. We judge whether it is a try/tap or not.

Thanks BillyMac, that's about when I got into reffing,