If the healer opens up with regen, it's the regen itself that seems to cause a hate spike on the healer even if they perform no other actions once the tank engages the mob. I found this out the hard way in an Ifrit fight, upon casting regen on tank beforehand I thought it would be a good move to do to give them a bit of HP regen as they ran in to hold the mob, but once they engaged the one tick of HP regen went off and all the hate was on me for a bit.