ZeroTier doesn’t override the DNS service that the system uses by default.
You might get the desired result by configuring the system to prefer a DNS server that is accessible through your ZeroTier network. (eg: systemd-resolved in most Linux distributions can do this.)
Past that, you need to provide more details about your use case, like the application software and the DNS records that it expects to get.
Note that many geofenced apps, especially video streaming apps, now use DNS pinning in the same way that they use TLS certificate pinning.