I have played FFXIII-2 just now and to use the time travel, Serah needs to have an affinity with the chaos (as the encyclopedia in game says) which she has.
So in FFXIV, because our light and darkness are tied to order and chaos, and we need to change the history, so maybe we need to embrace darkness to be able to use the time travel (if it's a thing in Shadowbringers).