Yeah. run tmux as
tmux -2 (forces 256 colors)
In your tmux.config put
set -g default-terminal "screen-256color"
In your vimrc put
AND in your shell that tmux is running you'll have to put
My experience has been that it only works when you tell every single one of them to shut up and pretend they have 256 colors. Otherwise one of them will think they know better and fall back to 16 or 8.
But if your force it make sure you actually do have 256 colors available in the terminal. Otherwise you'll end up with some strange stuff.
It took me way too long to figure all of that out.
It got easier once I started building all three from source.
They are riddled with bugs in the older versions.
(apparently others have had success with "xterm-256color", but that did not work for me. You're just going to have to try.)