Using an exit node with a private DNS server on it


I have Home Assistant on a Raspberry Pi running both Tailscale and AdGuard addons.

Tailscale is configured so that this device is an exit node.
DNS in the Tailscale admin console is set up so that the exit node is also a global DNS nameserver.

When a remote machine is connected to the Tailscale network without using the exit node, the DNS server for the machine is set to the DNS entry in the console (i.e. the same one as the exit node), so DNS traffic is filtered by AdGuard but traffic goes out to internet via the plain device network connection (geolocalised in the country where the device is).

When the same remote machine is connected to the Tailscale network and uses the exit node the DNS entry associated with the tailscale tunnel is set to which seems to actually bypass the global nameserver set for the private network, therefore bypass the AdGuard service (but traffic is geolocalised in the country of the exit node).

Can someone confirm this?

Is there a way to activate both exit node and custom nameserver?

Exit node is a Pi running linux node version 1.36.0
Remote client test 1 is a windows node running version 1.26.1 (that cannot be upgraded)
Remote client test 2 is a iOS node running version 1.36.1

Thank you very much