Pardon but are you actually completing any of the Esuna casts in this video? I see the effect going off but it's not saying "Esuna has no effect!" over your head and you're not completing the GCD either.

I do agree that there is some general wonkiness as far as warning indicators and animation display vs. time of actual impact, but it doesn't seem like the server's actually allowing you to cast Esuna while running as you're claiming.