By default DirectAdmin doesn't allow mail to be relayed through the server unless the sender is authenticated. You can easily enough turn on username/password authentication if you want, but DirectAdmin also uses Pop before SMTP authentication to make life easier for your users.
If your server's been sending spam, lack of authentication is NOT the reason unless you made changes to allow it in your exim.conf file.
While you havent given enough information for anyone to say definitively, you should also make sure that you haven't put any domains on your server into the /etc/virtual/whitelist_domain file, as that's the easiest way to break email security and allow people who forge return addresses on your server to use it to spam.
Jeff
