This is where your issue lies. The animation never matters.
When the cast-bar ends, (as shown below) the effect has already taken place server-side. The on-screen graphic for my Cure II does-not-matter.
It's the exact same for any fight in the game, from Titan's land-side/weight of the lands. To Nael Van Darnus Ravens Beak in Turn 9.
THE END OF THE CAST BAR + YOUR POSTION = EFFECT
THE GRAPHICS/ANIMATIONS DO-NOT-COUNT
When fighting Titan in The Navel, you'll find that if you get out of the way PRIOR to the end of the cast-bar and NOT the graphical effect you'll never have any issues.
The only time you're going to encounter issues is if your latency is simply too high. With friends as far as Australia playing with 200-300ms+, and we've cleared all of the content available in the game so far bar; T12/13.
Using (/focustarget) is your best-bet, (also move it in your UI for a more convenient place for you) and WATCH FOR THE CAST-BAR.
As you can see below, even if I have an enemy targeted I can still see my focustarget's casting bar.
This gives you a wider-area of time to notice and react.
And most importantly, if you fail because you didn't notice. Don't be dismayed, don't 'blame it on the lag', learn from the mistake and try again.
That's why you're playing a game right? For a challenge, not for hand-holding experience.
It's the same for Hallowed Ground, it seems to be a completely intentional delay, similar to some of the ones in World of Warcraft.