We recently experienced an issue with Postfix not sending emails to the localhost (mydomain.com) when the DNS is hosted elsewhere. For example, email for mydomain.com is hosted by Google Apps and all emails sent by the Postfix server to firstname.lastname@example.org were not being delivered. Fortunately this was an easy fix.
Open up /etc/postfix/main.cf. You should see a line that says:
mydestination = mydomain.com, localhost.com, , localhost
Add the following line below it
fallback_transport = relay
Stop and Start Postfix and you should be able to receive emails sent by the server to *@mydomain.com.