The application layer on top - your containers - is where the commonality is, and is what is meant by hybrid cloud. The implementation, however, is delivery platform-specific (such as on-prem, AWS, GCE, Azure). OpenShift would need to be installed on the platforms you are going to use, and would not all be a single cluster. The idea of hybrid means that containers (or multi-container applications) can be migrated or scaled quickly, to allow for load or platform issues that occur. But they are not a single-configured cluster.
It is important to say, however, that the whole philosophy of hybrid cloud is to make such multi-platform use fundamentally simple and seamless to users. For many technical implementation reasons, an installed clusters is contained within one type of plaform. There would be further discussions about latency and other communication requirements across worldwide or nationwide regions. Typically, it is not recommended to install a cluster that is distributed geographically beyond a platform's region. Moving applications between regions is also simple and mostly seamless, but is normally container movement between region-contained clusters. While network speed and bandwith today are more amazing than ever, technology is still not quite at the level for a single-cluster-everywhere concept.
There are monitoring components (for initial data gathering) that must be installed and configured per-cluster, but you can architect a solution that provides consildated monitoring information. Implemetation discussions are more indepth than can be simple described here, but the general idea is that yes, multi cluster management and telemetry is available.
