It's the whole ZT/DNS
and when I tested ZT in the past,
It is just DNS. You have to have it on EVERYTHING if you go that route.
Or, you make the ZT network the same subnet and not different.
Just take your 10.0.0.0/24 and make it a 10.0.0.0/23 instead.
have the local DHCP server hand out 10.0.0.101-254
have ZT DHCP hand out 10.0.1.101-254
or use ZT Bridging
Lots of ways to skin the cat.