Yona seems like she is treating this as a fresh start. Naomi is really eager to get back to her world, and Liriel at first hates it here, but Yona just accepts the situation.
Azraesha is a pragmatic person who wants to keep moving forward. She is in control because she knows the most about our situation, and once she understands what's going on, she feels very comfortable in the rift. Her mentor tells us to take care of Rae, but that seems easy because she doesn't have an obvious personality flaw or anything we need to fix or work around. She's comfortable being either a top or a bottom, for various obvious reasons.
Naomi is a pirate captain. She left her crew behind, and she doesn't trust them to be fine without her. It's kinda weird she never mentions their names or anything specific about them, but that may be due to the limitations of the format rather than Naomi's relationship with them. You can tell Naomi is always a top because she needs to be in control. This is kind of a personality flaw because when someone goes against her she gets antagonistic and can't back down, and when she can't be in control she gets depressed.
Caitlin is a student. Her main conflict is her desire to learn versus her sense of decency, thus her character is a great fit for the game mechanics. She likes living in the house because she's learning so much. She feels guilty about causing problems for her world, but unlike Rae and Naomi (and I bet Yona, later on), Caitlin doesn't feel a need to return to her world. Rather than a bottom or top, she wants to learn and try new things, so she'll (eventually) do anything aside from dominate and control her partner.
Liriel is a prickly person, and probably a young elf because she starts off acting like a bratty teenager. In this story we crush her spirit and presumably build her back up to be a whole person. She wants to go away from the house, and go to a forest or something, but there's nothing specific in her world she wants to return to. I've read stories and played games in which characters like her get dominated, but so far it seems like we've been more perving on her. Her story seems to be less about us changing her, and more her maturing.
Yona obviously had stuff to do in her world, and I think she will want to go back and do it. It seems like she is comfortable fitting in to a place with preexisting rules and relationships, although the house is less established than she thinks. I was surprised and pleased that nobody is prejudiced against orcs, and she isn't prejudiced against the non-orcs. She reaches the obvious conclusion that the house is some kind of afterlife, which it kinda is, and so is able to set aside her ambitions to fit in here. I think once she gets comfortable, her conflict will be between her newfound happiness and the stuff she needs to do on her world.
