Does taking damage lower enmity?

[Steady]

This game does not have volatile enmity.

what you saw from FFXI was probably DPS not doing actions, thus losing enmity from enmity decay plus tank trying to pull hate back with abilities.

I don't think that's correct. http://wiki.ffxiclopedia.org/wiki/Enmity

Volatile enmity worked where taking damage lost enmity. It was why they modified shadows to shed hate when used. Anyhow... I'm pretty sure it doesn't exist that way here, I was 90% sure of it.