That's exactly right. CP trapped the "diagnose" instruction in the virtual machine to allow the VM to talk to the hypervisor. The "diagnose" instruction was convenient, since it was an opcode that was never used in normal programs - on a real (non-virtual) machine, it was used by IBM engineers to diagnose hardware problems and did different weird things on each different model of machine.

The normal SVC (supervisor call) instruction was the API for programs to talk to CMS, the operating system that was most commonly run on top of the virtual machines. It was actually possible to run several different operating systems on the virtual machines, including CP (the hypervisor) itself. Systems programmers would do that for testing new versions of CP on a live system.