While server ticks play a role, these delays are part of the ability used. Some abilities will register but only deal damage after a specific amount of time has passed. For instance, DRG's Disembowel takes a bit more than 1.5 seconds to actually deal its damage. Meaning that while the damage is registered on button press, if the target disappears or becomes invulnerable after it but before they take the actual hit, you will lose the damage.
If provoke takes some time to actually affect the target, it is simply because the delay between cast and effect is high enough. Some knockbacks push you immediately while others are delayed after the cast bar is finished.
There's also no specific rule as to why some abilities take longer than others. Animations don't seem to have anything to do with it, as actions such as Chaotic Spring take long to finish yet register their damage extremely quickly, whereas Wyrmwind Thrust's animation takes some time and its damage is dealt mostly in sync with it.
From what I've gathered from previous posts on the issue on Reddit, this game's tickrate is not much different from others'. The problem might lie elsewhere. In any case, I enjoy the fact that you react to cast bars and not animations and don't mind this at all. Cast bars are not always present and sometimes their damage doesn't snapshot when they're over, although this is rarer, so you may need to adapt to different situations.
I'd rather get the ping problem related to weaving oGCDs addressed first, as this would make the game feel and flow so much better. See here: https://forum.square-enix.com/ffxiv/...tions-normally.
I do agree that it is a bigger problem in PvP though and that it should have a specific solution for this mode at least, especially when it comes to Purify or things such as dying due to delays in the damage right after using an action like Sky High.