First a minor issue:
I was hosting a server to try out the new caves preview (non-dedicated server) and animations and looting feels really laggy. I got a friend to connect to the server and try it out and he said it felt normal (he usually plays on my servers at ~60ms). As the host it felt awkward and laggy - my ping reported 0ms.
It seems only the host can go between under and above ground. Me (host) going underground resulted in anyone connected being disconnected. And anyone trying to go underground (with me above ground) got an error message: "the server is not available", and was disconnected from the server. When trying to reconnect when I was under ground they received the same error message.
UPDATE (07/02/15 - 6.28pm):
Selecting game modes other than Survival (Wilderness, Endless) doesn't seem to work. The game defaults to Survival.
Create a non-dedicated server Have someone connect Have them try to go into a cave Have them try to connect while you are in a cave