Do I need to create the same VxVM DiskGroup on both machines?

No, when you create a Volume Manager DiskGroup, just pick one machine to create the DiskGroup on. You do not create the same DiskGroup on both nodes. After you create a DiskGroup, you can add it as a Resource to your VCS configuration. VCS will then use VxVM commands to import and deport the DiskGroup between the systems during Service Group online, offline, or failover.