Time out after rebounding FT miss

[representing]

Was just watching the USF and ND game and a situation popped into my head.

At the end of the game with 4.0 seconds left during a 1-and-1, ND's big guy was shooting and ND did not put anyone in the lane. USF puts 4 in the lane. Shooter made both, but this is a situation i had in mind:

If the shooter missed the second FT, a USF player rebounds. If he's calling time out just as he grabs the ball, does any time come off the clock? Would you tell the clock person to put 4.0 back on the clock if you think the player simultaneously called time out as he was grabbing and gaining possession of the ball? I don't know where this would be in the rulebook to look it up.