Before you read the result
What ZeroTier documents about these signals
Each point below comes from ZeroTier's own documentation, which states what every local configuration flag defaults to.
Allow Default is off until you set it
ZeroTier documents four flags in a network's local configuration file. Allow Managed defaults to Yes and lets ZeroTier set IP addresses and routes. Allow Global defaults to No and covers public, non-private ranges. Allow Default defaults to No, and that is the one that lets ZeroTier set the default route on the system. Left alone, your internet traffic never enters the virtual network, and this page shows the address it always would.
An exit node is something you build
ZeroTier documents the exit-node setup as two deliberate steps: a managed route for all traffic pointing at the ZeroTier address of a router node you operate, added in Central under Network and then Settings and then Managed Routes, and Allow Default enabled on each member that should use it. Until both exist there is no exit node, and a check reporting your usual address is reporting the truth.
Allow DNS is off as well
Allow DNS also defaults to No, so ZeroTier will not set DNS servers on a member unless you allow it. On a default join the resolver answering for this browser is whatever your operating system was already using. A DNS check naming your own ISP is therefore not a leak out of anything; it is the absence of a change you never asked for.
The IPv6 addresses it hands out are private
ZeroTier's RFC4193 and 6PLANE modes assign addresses inside the unique local range, which the documentation describes as not globally routable, with 6PLANE giving each device a block of its own and embedding that member's ZeroTier device address. Those addresses exist to reach other members. An IPv6 check against a public site still reports whatever IPv6 your own connection has.
Where the DNS reading gets platform-specific
ZeroTier documents per-platform DNS quirks worth knowing before you read a resolver line. Most Linux distributions do not do per-interface DNS resolution out of the box, which is what its systemd helper exists for, and on macOS resolution goes through dns-sd, where the documentation records that nslookup, host and dig are broken while ping works. A command-line tool disagreeing with the browser can be that rather than the tunnel.