Pretty sure you can attach to an already attached tmux session as well, which I believe has the same behavior that you’re describing. I’ve never used screen, is what you’re describing different than what I’m talking about?
You can get similar behavior in tmux by creating a new session with the "group-name" argument set to that of the name of the session you want to attach to.
having all windows in a single session synchronized is helpful when you share sessions with other users.