Maybe this Ultimecia could want time compression because of the first Final Days, developing an extreme cause of ptsd, paranoia and wanting to be in control over her own life and what happens around her.
Lol, would love it if our own Squall for this was actually a Hrothgar. xD
Oh no, I meant Ultimecia creates a parallel timeline of those timelines because those timelines are both already interconnected with our main timeline. Espon mensions how all three timelines basucally complete the timeloop and solidifies our own timeline without any cracks in the seams, if that makes since. Ultimecia wouldn't neccesarily be messing with those versions of the timelines, but ones where she interacts with them with the Crystal Tower.
Garlond Ironworks engineers have the memento/device that allows us to travel from the Source to the First. Its the means that creats the portal for us to travel between both worlds. And that's what I meant Ultimecia could steal in order to get to the First and gain access to its version of the Crystal Tower.
I never mentioned using the Source's Crystal Tower for time travel, but the First's. Ultimecia would gain the ability to exist in the World of the Unsundered, G'raha's timeline and the First all at the same time by traveling to the two former and then coming back to the latter. Thus establishing existence within time in three different timelines at once. And going from there, the Ultimecia that returned to the First would then use her Crystal Tower to establish a link to the other two Crystal Towers she used to travel to those two other timelines and thus create a gateway for her two past selves to come back to the present timeline on the First, use the rejoining technique Athena and Lahabrea demonstrated for us in the Pandemonium raid's story cutscene to make herself three times as powerful compared to your average Ancient. And then somehow compress all three timelines into one using the three Crystal Towers existing within all three timelines at once as a beacon of sorts, forcing time compression.