Most DR plans are typically based on bringing up a remote data center that shadows what is contained in your on-premises data center. But when you add the cloud you add a few new twists here:
First, you need to understand what happens if your cloud provider goes down, where else is your data kept and how redundant is the provider's own methods? Most of the major cloud providers have done a lot in this area, but still you want to understand their DR processes.
Second, you need to understand what links you have between your offices and their cloud, and whether they are redundant or not. I remember one large federal agency that had three ISPs providing connectivity to their offices in the Washington DC area. The trouble was all three had paths through one of the tunnels in Baltimore, 40 miles away. When there was a tunnel fire, they lost all connectivity (now they have four ISPs and have more information about their routes too).
Finally, you need tools that work across hybrid environments, where information in your on-premises data center is mirrored with the cloud, and understand the recovery time and the effect of the outage on these connections when disaster strikes.