JMUplayer wroteIn link above:
Player Out of Bounds
Violation called as soon as player leaves the court for an unauthorized reason (NFHS)
Violation called when player returns and is first to touch ball inbounds(NCAA)
Doesn't apply to the play you describe ("saving the ball while falling OOB") -- that's not "leaving of your own volition".
The rule difference applies on a play where the baseline cutter runs out of bounds (perhaps to set up the screen) and then looks to receive a pass from the wing.
In HS, that's (supposed to be) an immediate violation (as soon as the player runs OOB). In NCAA, it's a violation only if the player is the first (next) to touch the ball after returning.