Thanks for your question! This can be handled in a variety of ways - I like to keep things flexible so game mechanics make sense ICly for a variety of character types and situations. Generally, the character would be told that the portal was leading to their home reality - the return could be handled in almost any way you like.

Generally, I think people have assumed the character went home and was returned by feeling displaced again, though I would be open to characters who want consciously to go home and then return to Riverview being given a sort of beacon that would make it easy for the portal to lock onto them and bring them back when they turn it on. If you have any other suggestions or ideas that would work best for your character's plot, let me know and I'll see if I can come up with a way to make it work!