time out granted, or not?

[Theisey]

You deal with the penalty first, than ask if he still wants the TO.
Don't even grant a TO if the clock has been stopped for OOB run, incomplete pass, awarding first down, penalty flag on the ground or after a kick play ends until you know for sure the head coach or field players know that time is not running. If they insist, grant it after moving the chains, or spotting the ball for the next down.

Tell your wing to say this to the coach. "If you want a timeout after the next play then ask for it at after the next play ends." I would never, never take it upon oneself to stop the clock based on that next play request. Make him ask for it again.