No, you don't need to have the DNS populated on the other side, you need to configure DNS on that side to push lookups for that domain to the main site.

Config -> Networking -> DNS -> domain dns servers.

This process is usually performed by a non-Untangle DNS server that could support Active Directory, because that is providing a uniform namespace for all devices enterprise wide. If you're using Untangle's DNS you'll need to create a separate namespace for each site, and use the domain dns server feature on each Untangle to push name resolution for each namespace to the appropriate DNS server on the appropriate Untangle.

And of course you'll need to ensure the DHCP service is appropriately configured to support that.