To be fair, most GUI's have their issues, Asus included, where things are buried deep!
There is no reason for this to occur if you have set at the WAN and DHCP settings page the DNS entries you want to use.
The only remaining item is IPv6. Do you have both IPV4 and IPv6? DNS is separate for both, wonder if the router is handing out IPV6 addresses with the ISP IPV6 DNS server...
Certainly, when I configure IPv6, again, you can accept the default from ISP or set your own.
Interesting you bring up IPV6.
With the isp router, i disabled IPV6 as it doesnt seem to work at all when testing, and yet is fine on the NETGEAR.
However, i have just put the NG back to ISP DNS on V4 and disables IPV6 and on the test it appears to sill have V6 detected?
https://thumbsnap.com/jVBWH4e1
Edited to add:
Just put v4 DNS back to Cloudflare and Google and after another test, the ISP DNS seems to be gone, however, they are still detecting IPV6?
They all seem to take a hell of a route!
https://thumbsnap.com/oiREn384
Also, i thought i would manually set V6 DNS but on the router, there seems to be too many 'spaces' to enter them.
https://thumbsnap.com/EgF1MfLv
Yeah, just because you only single stack to v4, it doesnt mean cloudflare dont do queries over v6 to the wider internet, the sites are detecting the DNS outbound connections, which is how they check what DNS you are using. So that result isnt unexpected.