This blogpost will shortly describes the steps what I did when I did the ASR between my on-premises (VMM/Hyper-V) and the Microsoft Azure from DNS settings point of view. Reason why I did the following changes was that I want to update DNS records automatically and fast after the failover.
I´m currently rebuilding my demo environment and I already have S2S VPN up and running between my datacenter and Microsoft Azure. Next thing what I´m planning to install is Azure Site Recovery (with VMM). I wanted to create own VNET for the DR purposes in Azure so I´m going to configure VNET peering between ASR VNET and the VNET which has the VPN connection to the on-premises. This blog show the simple steps how I did that.