Playing with Time

You don’t. It’s similar to how GMs in Blades in the Dark don’t track every faction at all times. We only care about the PCs, the big picture looks after itself. They’re working on one event that will effect things for someone other than themselves (either another Faction Paradox group or more likely the greater powers)

In general missions that PCs are sent on are not linked, but with discreet goals. Much like how 99% of Doctor Who is not about time travel, it’s just a plot device to have a different location for the story they wish to tell. But then like giant robot anime - its not about the giant robots. Science fiction isn’t what the story is about, that’s just the stage.

So a few things to make it easier for the Grandfather (GM):

• don’t have missions on the same planet, you don’t even have to have them in the same galaxy.
• if you do, don’t have then on the same continent
• have them occur generations apart
• assume the larger powers fix otherwise unsolvable problems caused
• alternate multiverses, dimensions and universes are a thing, as are alternate timelines and time loops. Time sometimes naturally fixes itself, sometimes artificially.
• egregious paradox eats itself. Which is to say too many problems and the cause is removed. The completion mechanic and the group playbook paradox flag (usually caused by untethered flashbacks aka time travel) help with this.
• all that being said, this is never our universe. We haven’t had dalek invasions or a UN sponsored anti-alien task force. Let them kill Hitler, then discuss what the new timeline is. Or just make it splinter off into an alternate timeline.

Much like it's spawning franchise - Doctor Who - you should treat time as a place. Time travel is merely a device to start a scenario in a new and interesting setting. If you have players in multiple times, treat them as being in multiple locations instead. If they happen to effect each other's circumstances, use Metatime Lag as a form of slowly tracking the repurcussions between places.