Now that's odd.
When I use the DMZ I don't get such remapping. It's as if you had port forward still enabled as well as the DMZ.
Again, I can't teach networking here. I will share what I do to make my security DVRs work but that's it. Sorry if this upsets anyone.
From the top, I use the router defaults and NEVER USE WIFI FOR THE FIRST TRIAL. I change the IPs as needed then put the DVR/Security thing into the DMZ and I'm done. Works first time, every time.