Reviving this in the spirit of the Chronopolis Split Paradox.
Seems to me that the split happened in 1006 when Schala messed about. For the next 4 years i would imagine both worlds would be identical under the guidance of chronopolis. Then in 1010 Home Kid arrives back in time to save Serge of which then causes everything else to screw up leading to the Dead Sea. Belthesar would obviously know that Schala's interference would cause the dimensional split hence Chronopolis being set up to monitor it.
If we take what Belthesar says:
Serge... This world is not
the world you grew up in.
10 years ago, something
happened that put your very
soul teetering on the
balancing scales of fate...
with a fifty-fifty chance
of life or death!
This is when your future
was split in twain.
He doesn't specifically say that it was 1010 the dimensional split occured, merely it was 1010 where the differences started to occur due to Kid only going back in time in Home, i.e. the fifity-fifty chance mentioned.
Maybe im just missing something, but it makes sense to me.