This is my Theory about Caius based on seeing everything in-game and all DLC's + interviews with FFXIII-2's Lead Writer -
Here's something from the Lead Writer. "Although Caius dies in the final battle, we see him alive in the Secret Ending. This does not mean that there are multiple versions of Caius that have been manipulating events from a different timeline. Quite the opposite: the Caius that 'dies' in Valhalla (a timeless place) is the same one that we see in the Secret Ending. His is a paradoxical existence that already knows how the battle ends and will still not stop until he reaches that end. His 'death' only strengthens his resolve, as even this did not alter the course of events. The goddess died nonetheless, which is what he fought for all along."
Since in total, he dies twice (Main ending then Lightning DLC battle where you finish him as Chaos Bahumut and the caption comes up 'Chaos Bahumut Defeated! The Chaos Has Been Banished!') yet still appears in the 160/160 Secret Ending... my Theory is this.. The 'real' Caius only appeared a few times - 1) In Noels time before he left. 2) When he fights Noel and Serah separately in The Void Beyond. 3) When he fights Lightning in the DLC in The Void Beyond. 4) Secret Ending to main game. All other Caius's were the Paradox one while the 'real' Caius was watching from Valhalla/The Void Beyond.
Now, the Paradox Caius fights Lightning in the beginning of the game, then fights her in the first non-controlled battle for the DLC *he sees her vanish into Chaos after striking her down and the Dialogue "Lightning is dead, I killed her with my own hands." is played* Then he goes and confronts Noel & Serah in the different Era's in the game, then battles them in 500AF and dying in Valhalla. When this one dies, the 'real' Caius unleashes Chaos from The Void Beyond/Valhalla *Secret Ending*, after that Lightning appears in The Void Beyond and the rest of the DLC takes place with Caius finally being killed by Lightning, then Lightning sits on the Throne after cutscenes.....
That's my opinion on it, it's the best Theory I can come up with that has the least amount of contradictions to it, since after all, time in Valhalla does not flow normally..