Why are you trying to apply rules regarding fly balls to a tipped pitch by a batter? Any ball that is tipped by the batter and is not sharply and directly to the catchers hand or glove and is caught by the catcher is an out.
From an older USA rule supplement, and no the rules have not changed.
Notice it specifically says "or if the catcher moves their glove/mitt to catch the ball after contact with the bat.".
RULES SUPPLEMENT
22. FOUL BALL / FOUL TIP
The reference of the “height of the batter’s head” as it relates to a Foul Ball and Foul Tip no longer applies. This change, instituted in 2006, allows more opportunity for the catcher to obtain “outs” by catching foul batted balls the same as the first and third base person who is playing closer to home plate. Umpires only need to judge whether the ball moves from the bat “sharply” and “directly” versus a ball that has a perceptible arc and / or if the catcher moves their glove / mitt to catch the ball after contact with the bat. The definition of a foul ball has not changed. However, a foul tip is now defined as a batted ball that goes sharply and directly from the bat to the
catcher’s glove / mitt or hand and is legally caught by the catcher. It is not a foul tip unless caught and any foul tip that is caught is a strike, and the ball remains live in Fast Pitch and Slow Pitch with stealing. It is not a catch
if the ball rebounds off the catcher, unless the ball has first touched the catcher’s glove / mitt or hand. Again, a foul tip can only be caught by the catcher. Examples of foul ball and foul tip follow:
A. A foul ball with “perceptible” arc goes toward the catcher’s left and the catcher moves their glove / mitt to catch the ball. In this situation, the batter is out and the ball remains live just as it would when
B. The foul ball rebounds from the bat with a “perceptible arc” shoulder high and the catcher moves upward with the glove / mitt to make the catch. In this situation, the batter is out and the ball remains live just as it would when any other fielder catches a foul fly ball.
From an older USA rule supplement, and no the rules have not changed.
Notice it specifically says "or if the catcher moves their glove/mitt to catch the ball after contact with the bat.".
RULES SUPPLEMENT
22. FOUL BALL / FOUL TIP
The reference of the “height of the batter’s head” as it relates to a Foul Ball and Foul Tip no longer applies. This change, instituted in 2006, allows more opportunity for the catcher to obtain “outs” by catching foul batted balls the same as the first and third base person who is playing closer to home plate. Umpires only need to judge whether the ball moves from the bat “sharply” and “directly” versus a ball that has a perceptible arc and / or if the catcher moves their glove / mitt to catch the ball after contact with the bat. The definition of a foul ball has not changed. However, a foul tip is now defined as a batted ball that goes sharply and directly from the bat to the
catcher’s glove / mitt or hand and is legally caught by the catcher. It is not a foul tip unless caught and any foul tip that is caught is a strike, and the ball remains live in Fast Pitch and Slow Pitch with stealing. It is not a catch
if the ball rebounds off the catcher, unless the ball has first touched the catcher’s glove / mitt or hand. Again, a foul tip can only be caught by the catcher. Examples of foul ball and foul tip follow:
A. A foul ball with “perceptible” arc goes toward the catcher’s left and the catcher moves their glove / mitt to catch the ball. In this situation, the batter is out and the ball remains live just as it would when
B. The foul ball rebounds from the bat with a “perceptible arc” shoulder high and the catcher moves upward with the glove / mitt to make the catch. In this situation, the batter is out and the ball remains live just as it would when any other fielder catches a foul fly ball.
