quit tmux server and end all running processes
I have found an alternative by adding a line to my tmuxinator config:
pre: pkill -f "^python manage.py run_gunicorn"
The ^ at the beginning only matches processes which are starting with that command. Without it you would also kill the tmux process as well.
This does not solve the problem with remaining background processes, but it kills any old processes when restarting the tmux session, which is an acceptable workaround in my case.