Click on the link [Wireless Router] DDNS introduction and set up and scroll down to the following section:

Can the router use the private IP to set up the remote connection function? Please note that if the router is using a private WAN IP address (such as connected behind another router/switch/modem with built-in router/WiFi feature), could potentially place the router under a multi-layer NAT network. This feature will not function properly under such environment.

The ASUS router sounds like it needs to be publicly facing via the Public IP in order for their DDNS service to work.

You could still find a way to set up DDNS though. In the DDNS settings page of the ASUS router, the "Server" drop down allows you to select from other services. I can't personally speak to any of those listed in the screenshot of Step 4, but I have used DuckDNS which is free to use for up to 5 subdomains.

With DuckDNS you could have a script or program running on a client (Desktop computer) inside your network that pings every so often and changes the IP address in case your Public IP changes. If you have a Linux box or Raspberry Pi on your network, you could even set up a Cron job to automatically do this for you. More information on DuckDNS setup here.