The router is not directly involved in a dns query except, we’ll, the routing if it’s an non local IP. The DNS ip addresses is propagated either via dhcp together with the clients or directly configured in the client. That said: most routers serve as dhcp server at the same time. Perhaps your router is configured to always provide your ISPs DNS as primary.

How the client handles the decision which to query I honestly don’t know and I guess that’s why you and I made different experiences!