In general accepted practice is to use example.com or example.net when posting examples. In fact those two domains are actually reserved for such use.
I understand your need for privacy, but I have no idea if those postmaster addresses are to or from domains on your server. Nor do I want to spend a lot of time trying to figure out what is a hard-to-understand situation at best.
Hopefully someone else will respond.
I could log into your system and fix the problem and tell you exactly what caused it, but I offer that only as a commercial service. What I do not do is answer questions in private messages on the forum... I feel that if I'm offering my valuable time to help people then I want to do that on an open forum where many can benefit.
In the meantime, please see the rest of my original reply; it does contain information on what you can do, and in fact, it tells you how I'd start if you did hire me, probably what almost any administrator would do.
Jeff