I moved over to world 2 and upon entering the volcano, the map was revealed and it was identical to the one I had in world 1. This must be a bug, otherwise you could have a permanent base on the volcano regardless of world hops.
Steps to Reproduce
Played a new SW as Wilbur, explored volcano, unlocked Woodlegs, played second world as Woodlegs, went to volcano
Played a new SW as Wilbur, explored volcano, unlocked Woodlegs, played second world as Woodlegs, went to volcano