Color differences between normal terminal and tmux terminal

In ~/.tmux.conf:
      set -g default-terminal "screen-256color"

In .bashrc or .profile:
     export TERM=xterm-256color
   alias tmux ="TERM=xterm-256color tmux"

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Updated: 5/11/16

Actually, everything works okay with just the change in ~/.tmux.conf...

I removed:
export TERM=xterm-256color from .bashrc
alias tmux="TERM=xterm-256color tmux" from .profile


Discovered this when trying to overcome the following problem created by running tmux in xterm-256color mode. Matlab in commandline mode inside tmux does not recognize home and end keys etc. Displays them as "[~1" etc. rather than moving the cursor.