I meant the factions themselves - not the NPCs but for BGS stuff.
The first faction (The one that owns the station from which you first used the Colonization contact) appears immediately as you make the claim, or soon enough.
The third place faction will be the one that your squadron is currently pledged to. The other two factions, I don't entirely know. These appear after 1 day (I think after the BGS tick) Someone in our group completed his outpost rather quick and it spawned
1st place: Faction that owned the station where he colonized from (The one that appeared immediately)
2nd place: It was the 2nd place faction in influence in the system he colonized from
3rd place: Squadron PMF
4th place: Random anarchy from the original system too
2nd to 4th place appeared within a day