You can do a quick imperfect test to see how bad it is by playing the game side by side with two computers or clients.

Both of them have to communicate to the server first, then send the information to the other client. A little bit of latency here is normal and expected since we can't defy the laws of physics or anything. FFXIV is really bad though.

If it were just animations, they wouldn't be so far out of sync, they'd be relatively similar. You just wouldn't see the effect until it was supposed to happen.