After a lot of searching, I'm still clueless as to where the problem lies.
By the way, it does work with my system user, but for some reason I can't log in with that account in squirrelmail. It just doesn't accept my username/password.
When I send a mail to both type of accounts I can also see a difference in the mail.info log:
May 22 17:55:24 mydomainname postfix/local: 5152556564: to=<email@example.com>, relay=local, delay=2.4, delays=0.33/0.18/0/1.9, dsn=2.0.0, status=sent (delivered to maildir)
May 22 17:55:24 mydomainname postfix/pipe: D605A5655E: to=<firstname.lastname@example.org>, relay=maildrop, delay=3.6, delays=1.6/0.1/0/1.9, dsn=2.0.0, status=sent (delivered via maildrop service)
One is delivered to maildir, the other delivered via maildrop service.
From the google searches I made, I'm getting quite convinced that if the latter were working, the log would show that the mail directed to user
wouls be delivered to maildir as well instead of via maildrop service.
I hope this helps you guys who are trying to help me.