Well, it can't be the Chrono Cross' fault. It is stated to only have the power to unite things, unite minds, heal (could be mental or physical) and merge things that were once two or just reset them to their original.
Anyway, Schala's ending journal passage hints that she believes in reincarnation, and that would mean that Serge could be reincarnated anywhere. Hence, she is looking in our dimension is well. It was a really ingenious thing to do - connecting the journal to the ending cinematics. If you understand the journal, then you'd understand the cinematics. Probably from her fruitless effort in the present of our dimension, the turning back clocks could mean that she will look in it's past.
Her goal is to find Serge (but I sometimes think Magus anyway) in any time, in any place, in any reality.