You can do this easily in tmux by having them work in separate sessions. This allows them to have their own set of windows.
I use an ssh alias at work to always log me into my tmux session if tmux exists on the server
ssh -t 'tmux new-session -A -s mySessionName || exec $SHELL -l'
I shared this with a workmate and he just changed the session name and we both have our own tmux sessions.