The shared responsibility model is a well accepted tool to help raise awareness that while cloud providers are responsible for the security of the cloud, cloud buyers are responsible for security of their data in the cloud.1
You’re almost certainly responsible for the security of data on your premises and in the cloud. As your workloads migrate to multiple cloud providers, questions you likely will want to address to ensure you are confident in the security of your data in the cloud include:
1See: various Shared Responsibility Models: Amazon Web Services, Microsoft Azure