Yeah,it is super strange. We were thinking my friend lost all his progression. Strange as none of the other Trine games worked this way. Let's hope it is a bug and not a feature.

Here is a tip so you can carry over your saves. The non-host should hit continue save and join through that menu. Joining someone through invite just makes a new save altogether. Its bothersome but its a workaround. The save even remembers who hosted last time so they can join through that.