Any changes to ~/.bashrc or even ~/.tmux.conf would not reflect in any newly created session unless you terminate all sessions and start afresh. In screen, every new session starts from the current host environment which is more convenient
In fact I was a bit surprised that .profile ran on every created pane, as naively I would not have thought that would be a login shell.
not sure about the rest, I did read the man page again, and wow there is a lot more configurabilty than I first thought, however I found nothing great, the best I could come up with is.
bind c 'source-file /home/xxx/.tmux.conf; new-window'