If modern (contemporary writing) time travel doesn't include a multiverse component, it's essentially bad lore.
The Exarch existed in a future where the eighth umbral calamity had happened. He travels back to the past to stop the calamity with no suggestion that he is entering some alternate reality in the process. By succeeding, he should therefore have no reason to travel to the past in the first place. Ergo, the calamity must happen.
I hate to go the Emmett Brown, route, but that right there...
https://i.imgflip.com/34m1v7.jpg
... is a paradox.
Good time travel stories eliminate the element of destiny (the all-important question of: was Harry always in the past to summon the petronus to save himself? How did Harry get to the past to summon the petronus if he had never been saved by it in the first place? Destiny) by generating multiverse "ripples" whenever the time travel occurs - all actions, no matter how small, generate alternate realities, each of which can be dealt with individually without necessarily stomping like elephants on the bodies of the previous ones. The time travel in FFXIV doesn't deign to dally on those details, so the consequence is that it is fairly branded ludicrous storytelling.