If that's happening, it sounds like you're moving too late. First time I encountered this was Titan Extreme, where it forced you to learn that you can't dodge last minute. You never finish casts, you move immediately and there's no such thing as jumping out of mechanics. Everything you do, casting spells, dodging, popping cooldowns or applying things (virus, disable, sacred soil, etc.) has to account for the possibility of a 3 second check (server tick). If you fail that check, you're hit or the affect doesn't apply in time. As long as you keep that in mind and apply things accordingly, you won't die. FFXIV is more timing based and doesn't apply instantly like most other MMOs.
Unless your ping is just that bad, which is something you would need to fix and has nothing to do with SE.
