Q: If my virtual networks are in an Azure resource group, does that mean virtual machines that use the virtual network need to be in the resource group of the virtual network?

A: No. Virtual networks are region-based. When virtual machines are created and placed in a cloud service, the first virtual machine in the cloud service chooses a virtual network to be part of; all future virtual machines in the cloud service are part of the same virtual network. Virtual machines can use virtual networks that are in the same region as the virtual machine being created and don't need to be part of the same resource group. A virtual machine can't be part of a virtual network that's in a different region; this is enforced by the regional network manager component.