Chrono Cross' ending is too vague to say anything for sure. The Compendium's whole theory on it relies on the assumption that Chronopolis wasn't sent back in time, but rather being connected to the past through a temporal rift. And that eventually, Chronopolis workers would just appear at the Sea of Eden to colonize El Nido even though Chronopolis doesn't exist anymore. Personally I don't believe that at all, as it's stated directly in the game that Chronopolis was sent back in time, and the fact that the supercomputer FATE terraformed El Nido, not the workers. Mere humans cannot create islands out of thin air, especially not without Chronopolis.
Another theory is that the "optimal" version of each person was used for the ideal timeline, but that creates problems because some people would be from one dimension and others from another, even close acquaintances, which means they technically wouldn't know each other.
Or, perhaps only one dimension was preserved while the other was simply erased. This also creates problems. If Another World was preserved, which would make sense as it's the "original" timeline, Chronopolis exists, and Serge would be living in a world he wasn't born in. If Home World was preserved, that means the Acacia Dragoons still met a grisly fate, Fargo is still a pathetic shell, etc.
It's a shame they gave us so little to work with, and I haven't a single theory that has no complex contradictions. I presume not even the writer himself ever came up with a perfect solution.
