First, you need to add some macros to the top of your Exim config file. These just make the director (router) and transport below a bit cleaner. Obviously, you'll need to edit these based on how you configured and installed Mailman.
# Home dir for your Mailman installation -- aka Mailman's prefix # directory. MAILMAN_HOME=/usr/local/mailman MAILMAN_WRAP=MAILMAN_HOME/mail/mailman # User and group for Mailman, should match your --with-mail-gid # switch to Mailman's configure script. MAILMAN_USER=mailman MAILMAN_GROUP=mailman