As a Roblox developer, it is currently impossible to teleport a player back into a private server [the roblox ones (NOT A RESERVE SERVER)] after teleporting them to a different universe.
Adding this would allow developers to put groups back into a private server after teleporting them out, for example in my game I use universes for gameplay and have a lobby as well, after each set of gameplay if they choose to go back to the lobby it will bring them into a public server even if they came from a private server.
In terms of the arguments it can just be the playername of the owner of the PS