This may be a game management issue, but help me out if you can. NFHS rules.

Home Team A takes the court approximately 20 minutes prior to game time and begins its pre-game routine. Timer starts clock countdown. (20 minutes) Team B comes out of locker room two minutes later and requests of Team A Athletic Director (management) that clock be reset to 20 minutes to allow them their full warm up time.

Denied.

What rulings apply here, if any?

This is more of a local league rule than an NFHS rule. In fact, NF says nothing about warm-up time, except that (a) officials' jurisdiction starts at 15:00 and (b) rosters and starters must be in at 10:00.

I know that at my school, we do 15:00 between JV and V - starting when the JV game is over.

If game time is 8pm wouldn`t you start warm up at 7.40pm subject to any programed stoppages for introductions etc.

If game time is a set time! I think that it is up to the coach or his assistant to keep track of the time! I have been at gyms where if the scorer and timer are in the gym, they may set the clock to 45 minutes(7:15 for an 8pm start).
To the original question! I would say "Sorry Coach"

AK ref SE

Agreed. This is entirely a game management issue.

15 minutes (30 mins. for most college games)is the only time we need to be concerned with. That's the time we should be on the floor and ready to go. If they (teams) want to start warming up the day prior, go for it!, who cares!!