One of the users on the system has a CatchAll-email address. He receives all emails, even those intended for users of another site on the same server. The MTA on the server is postfix.

Please check if the domain of the users that receives all emails is the same as the domain $mydomain in /etc/postfix/main.cf. If this is the case, change $mydomain and run

postfix reload

on the shell.

You should never enter a domain that is used for a virtual site on the server as $mydomain in /etc/postfix/main.cf!