
The time-travel cultists began shipping people from one reality and time-line to another after the rupture of the time-space continuum during the black budget research operations of World War II. These cultists believe all sorts of strange shit, but that's because they've got an entirely different frame of reference for understanding events.
Refer: The Testament of Orpheus.
Likely one of the primary conflicts being the inability to anchor either in past or future to a specific timeline, time travel cultists find cause and effect become ripples, not precise constraints. All is cloud, conjecture, and plausibility, nothing can be unstuck from time in all timelines, no one is their own father in all worlds.