As this is the first time I have done this I am looking for clarity that I am doing it correctly, I have looked around blogs etc and I obviously think I am, but no joy getting it working yet.

I currently have a traditional Active Directory running Windows Server 2012 R2, I also have an Azure tenancy that has a Windows Server 2012 R2 instances provisioning that I would like to make my Azure DC. The vNet configuration has been completed, and my Site to Site VPN connection is up and working correctly. IP connectivity is working fine as I can RDP from my Azure VM's to the on-premise VM's, latency etc is fine.

The questions;

When I configured the vNet I "registered the DNS server" as outlined in all of the documentation, these registered DNS server are then automatically assigned as the primary/secondary DNS servers for instances that connect to that vNet - Correct? Think so as I have tested. So I set the vNet DNS servers to my on-premise DNS servers so that I could resolve my domain and join the machines to the domain.

When I do an NSLOOKUP the instances are using the on-premise DNS servers but they cannot resolve properly. 

Can someone clarify that this is the correct way in which DNS should be configured in order to do this? I have tried all sorts out of frustration for example, creating FLZ's with static entries (while changing the vNet DNS to the azure instance), then configuring forwards on the azure DNS to the on-premise servers.

P.S - I can see on my ASA that UDP53 is fine between the two servers.