Nonononono
Why do I always end up explaining inexplicable things
Anyway
A save is created with a bunch of differently colored 64x64 cubes dividing the bedroom or whatever
When you take that save you tell the others what cubes you want to work in.
YOU NEVER LEAVE YOUR CUBE FOR THE NEXT REASON
Once done, or whenever, you load the saves from all the participants thus having the whole thing come together.