The first time you try using irssi with tmux you might notice that on screens larger than 40 rows the refresh functionality does not work. This is a known not-really-an-issue tmux requires a particular term and is quite clear about it in the docs (if you read them I did not). Found the solution here, when you start tmux set the term for it correctly:
alias irssi='TERM=screen-256color irssi'