firstname.lastname@example.org R=localuser T=local_delivery defer (13): Permission denied: cannot create /home/diradmin/Maildir/that will mean that the receiving mail server is doing a sender check (or bouncing the email). You can satisfy this check by adding:
diradmin: :blackhole:to your /etc/aliases file so that the exim accepts emails to "diradmin" (but will just dump them into the abyss we call the blackhole). If you actually want to get the emails to diradmin, then change :blackhole: to be a valid email address, eg:
diradmin: email@example.com the /etc/aliases file.