On top of your default admin user, create a user called dns-cluster on the primary DNS server.
cd /usr/local/vesta/bin ./v-add-user dns-cluster [password] [email] default [firstname] [lastname]
Run cd /usr/local/vesta/bin && ./v-add-remote-dns-host ns1.remote.com 8083 admin P@ssw0rd123.
This instructs the current DNS server to push the DNS zones for admin user to the remote DNS server, ns1.remote.com.
The current server will now push all it's DNS zones to the remote DNS server specified, and the DNS zones will be stored under the dns-cluster user account.
Repeat the steps for all of your servers.