After playing through this part of the script, it seems that...
1. Orlha and Tia were not duplicated, but rather thrown to either dimension.
2. There was only one original girl, who believed she had a sister after the split.
Tia is in Another World for some reason, why Orlha's in Home. Somehow, their Blue Brooch broke and they were separated across the dimensions. For reasons unknown, Tia fell unconscious and ill for no apparent reason (I blame time).
Anyway, this is quite a little mystery that hasn't been unraveled. The game makes a lot of weird dialogue concerning them; really enigmatic.