There's a huge deformed river flowing through the air, the location of the river is below the castle of Ulti.

What do they call it? Time is a river?
The basic of time travel is that there are different timelines, flowing into one river, tending to co-exist. As we have seen events in the timelines but I wonder where does each timeline/river bifurcate or split?

Why do you think the castle is near the river? The castle was from somewhere in time (neither past or future) , it wasn't present.