If the healer is spamming heals or over healing then they will attract the attention of the mobs. The healer needs to not develop OCD at keeping the tank at 100% but allow them to drop just a little so that when they heal they do not "waste" any healing as that is like a red flag to a bull as far as aggro is concerned.

If the healer does get aggro then they must not panic and run! Just stay calm and stay put to allow the tank to regain the aggro. If needed use fluid aura to knock back a mob and repose another.

The healer (as well as all others) need to keep an eye on the aggro meter - not just the tank.