By default, tmux uses a 500 millisecond escape-time, which causes problems with multi-function keyboard keys1.
Set it to 0 instead:
set -s escape-time 0
Footnotes:
1
For example, I have my <caps lock> key mapped to <ctrl> on hold, and <escape> on tap.
With tmux's default escape time, tapping it without waiting for half a second before the next key press results in a <ctrl> being sent instead of an <escape>.