0.3 seconds left — Would a dunk from a throw-in or off. rebound of FT miss count?

[Blindolbat]

I had a game last week using NFHS rules with .4 on the clock.
On the inbounds pass, the receiver catches the ball just after elevating at the free throw line. He floats about 10 feet through the air while controlling the ball in the hand and then shoots all before the horn goes off. I didn't allow as I felt the clock did not start on time and that's the only way the ball could've been in his hands so long.
Partner said I was wrong to wave it off because with .4 a player is allowed to catch and shoot.