Perhaps what Belthasar means was: Serge's survival differed the home world's future from another world.
But that's only my thought, it seems it is even offcially confirmed that Serge's survival was the reason why the dimension was divided.
Hmm... unless we say that splitting the dimensions and dividing them are two seperate things.
That is, in 12000/2400 events happen causing the dimensions to split. There is Home world and Another World. They are perfectly the same, however, and Chronopolis is purposely keeping them that way since it is a single city that came from two different futures. Who knows what would happen to it if one of those futures were changed (like what happens in Home World)?
Though separate dimensions, for all intents and purposes they are the same. Indeed, from a sci-fi standpoint, it is pretty standard for things to coexist in the same place but be out of sync with each other, and so be separate.
Serge's life and death situation, however, is what caused the two to diverge. Before one couldn't travel between the two before what was there to travel to? How could one even tell if one was in Home or Another? But afterwards, the two became separate things capable of different futures.