The rendering of multiple cursors is really buggy in tmux + vim, to the extent that it's hard to tell what has been selected.
I have used this command for the purposes of changing a variable name. It could be better but gets the job done most of the time.
> :.,$s/\<<C-r><C-w>\>//gc<Left><Left><Left>
Short demo: http://cl.ly/image/403j153F3u1h