Normally in co-op writing and roleplay, it is terribly bad manners to write for somebody else's character (put words into its mouth, make it do something) without permission. But with shared characters, you don't need permission. You should try to keep them in-character according to their Twine profile, but it's fine to make them talk or act however you need them to.
An example of a shared character could be a waiter at a restaurant: he's not important to the story, we just need someone to bring the meal and go away again without a writer having to take specific responsibility for controlling him. (In this case he is shared by default, but named, more developed characters can be shared too.)
Members may not co-opt shared characters or concepts for themselves or claim ownership of them. Ownership is considered to reside with the group as a whole.