I've done it both ways. The only thing I didn't like about putting them in their own separate tubs right away was having 'x' more tubs to keep paper towels damp. It's super dry here so that was kind of a pain. But I liked that I could ID each one right away and not have to wait till they shed.
I didn't consider the different geo locations affecting humidity...that being the case it may well be easier to leave them together. I'm on the hot, humid east coast, so damp paper towels the first day or two is usually plenty.
Lucifer Sam, Siam cat...
Always sitting by your side,
Always by your side...
That cat's something I can't explain...