Before you read the result
What Tailscale documents about these signals
The points below come from Tailscale's own documentation on exit nodes and on how names are resolved inside a tailnet.
Without an exit node nothing about your address changes
Tailscale describes itself as an overlay network that only routes traffic between devices running Tailscale, leaving public internet traffic untouched unless an exit node is configured. If you never selected one, this page will report the address your connection always had, and that is the product working rather than failing.
Exit nodes are opt-in at both ends
The documentation states that every device must explicitly opt in to using an exit node, and that a node has to be approved before it can act as one. Two separate decisions therefore stand between installing Tailscale and seeing a different address here, which is more than most people expect.
Name resolution inside the network is separate
MagicDNS resolves machine names within your own network to fully qualified names built from the machine name and your network's own DNS name, and Tailscale documents that the nameservers you configure receive the queries MagicDNS does not handle. Those are two different populations of query. Only the second reaches the public internet, and only the second is what a DNS check on this page can observe, so a reading here says nothing at all about how your own machines find each other.
An unchanged reading is the documented outcome
It is worth stating plainly because it is unusual: on Tailscale without an exit node, a check that shows your own address, your own resolver and your own country has not found a leak. It has confirmed the scope of the product, which is connectivity between your devices.
What changes the moment an exit node is selected
Once a device routes through an exit node, public traffic follows that path and the address here should become the exit node's. That is the point to rerun these checks, because it is the only configuration in which the page is measuring what most readers came to measure.