All endings are in a way incorrect. On the GPG forums I once read that GPG had said that the Cybran was "most" correct.
Based on the FA intro movie, the Aeon one is most correct. If you're going for what's most realistic compared to our real life, don't bother: we've got alien bombers coming from a rift in the space-time continuum that's not in the direction of which Black Sun fired or at the exact origin of the weapon firing. We've got 40m tall weapons of doom going from one end of the galaxy to the other in a second. We've got one bloke transferring his brain to a jar in order to live for 1000 years and having an artificial intelligence as his sidekick while on the other end space-hippies go mental and want to kill everyone. Someone transferring to a ghost-like phase and back is not that far fetched in that regard. Also, this person turns into a ball of energy in order to seal that rift from which 400 Asswashers started washing Earth's ass earlier. One person did that.
What the timeline film mentions, is only that Black Sun is fired,
not by which faction. What's on the wiki is an assumption that's not based on what's actually mentioned in the timeline film.
The film also mentions the Death of Riley on X-Day, as well as the Seraphim ravaging Earth. It mentions the disappearance of Burke too (and she returns in mission 2). In addition to this, the Avatar-of-War is gone too, but you see that because he's just not around, not because he's explicitly reported dead.
Also in the story timeline film: how the Aeon split between the Order and the Loyalists, who had to go into the war guerilla-style. That's the only fully human faction essentially at war with the other human factions. The Cybrans are not at war with the UEF or vice versa. The Loyalists join in the alliance as well to fight against the Order, Seraphim and QAI. QAI uses Cybran units but his ACUs are remote controlled (It mentions it when you kill the Cybran ACU in mission 2).
You can see in any mission intro that the planets supposedly destroyed by the UEF firing black sun, are still around. Most notably Seraphim II. With the UEF firing, the Avatar was actually there and got killed that way. In the Aeon story, you get to kill him in the final mission. In the Cybran story, he's not actually around (or is he? I didn't finish the Cybran story).
On the thing about the UEF being the only one actually firing Black Sun: yeah, them firing gives the biggest fireworks, but in the SupCom intro missions, Burke/QAI mention being able to repurpose Black Sun for their own purposes. Capturing it in the respective final missions does lead to it firing, but essentially for a massive data payload across the quantum network. That's still Black Sun firing.
This is dotswarlock's series of SupCom books and he also had to deal with the end and start of the two stories. I absolutely recommend to read this and take this as the official story:
https://docs.google.com/file/d/0B_LpCNQ9Qch-eE5TbU4tODI5Y2s/edit?pli=1Books 1-4: before SupCom.
Book 5: SupCom.
Books 6-9: Between SupCom missions and FA missions.
Book 10: Between FA-5 and FA-6.
Books 11-13: After FA, and including what SupCom2 should've been as a story.
A short summary:
Combined win between the UEF/Aeon/Cybran against the Avatar-of-War, who's turned into the a godlike all-powerful commander. Burke next delivers her message to try and end the war. Riley is killed by one of his own men because he doesn't listen to Burke's call. The Seraphim attack next, with help from QAI, while the Cybrans take time to even figure that out.
Brackman figures out first (immediately) but he's forced to take time in order to deliver the news about QAI to everyone instead of one single group of people at a time. The Seraphim manage to take control over the Aeon because a willing and unaware pawn becomes the head of state. Burke is in a coma after delivering the message and is hidden carefully while the few loyalists start the guerilla war.
Later the Cybran and UEF start an alliance, while the Loyalists join a bit later. Then two books about how the old ACUs are replaced with the new versions (essentially counterparts to the Seraphim). After that, the first four missions and then book 10