tmux 1 session accessed by multiple terminals, each with a different visual state

I use a tiling window manager and someimtes have 6 or 7 shells open at once. Locally, I use tmux purely as a multiplexer because my preferred terminal does not have one (which I like). I would like each terminal that I open to access the same tmux session (which I have working), and I want to assign each terminal to a different window (1-9) in the same session. However, if I open two different terminals that share the same session, any visual state change to one will affect the other. For example, if I move one terminal to window 2 the other terminal will also move to window 2. This makes sense, but I want it to not be that way. How can I get each terminal to share the same session but have independent visual states? If this is not possible, do you have any suggestions that are close to my intended workflow?