Battle Tower Timing

[RB Golbat]

My opponent has Damage Bind Ampharos out on the field and my Active Garchomp C has 3 Damage Counters on it, with Battle Tower as the current stadium. When Garchomp Levels up, does Battle Tower remove the damage before or after Healing Breath would activate?

 

[PokePop]

The existing effect of the Stadium would be applied before the optional effect of the Power can be triggered.