Reset it? The clock was stopped. You mean run some seconds off? How many?
IMHO (for what it's worth) H can't ever "grant" a timeout. That's the White Hat's job. H can stop the clock to let the White Hat know a team is requesting a timeout, but the White Hat can start the clock right back up once he knows why H stopped it if the team is out of timeouts.
I don't know about the first round after the game, either. This sounds like a failure of the CREW to make sure everyone is on the same page regarding timeouts. On any timeout, after we've marked our cards, we're visually verifying with each other what the current timout situation is. If someone has something different, they come in and see who missed what.