Possible different micro ops for different semantics.
They also don’t mix instructions sets within the same process - the diagram I saw had ARM Linux as a guest under z/VM or KVM. For generations now no OS (not VM, not z/OS) hasn’t seen the bare metal machine, only ran under the PR/SM hypervisor, which is what does the logical partitions now.
In order to properly run OSs for the 360 and 370 generations, s390x also has instructions for setting up CPU flags to more precisely emulate older machines. From an s390x binary you can, IIRC, do a jump to an address telling it that, from the jump forward the ISA is the one of a 360 until it encounters a return, which restores 390 mode.
I found this article with the diagram that you mention: https://wccftech.com/ibm-worlds-first-dual-architecture-proc...
The diagram is the last picture, and according to it you choose the ISA at the VM level: either Linux on s390x or Linux on arm64, but not both on the same VM.
Interesting that z/VM doesn't seem to support spinning up ARM Linux VMs, at least according to this diagram, but it does support bringing up s390x Linux VMs (the LinuxONE Community Cloud creates Linux VMs under z/VM). Also, it looks like z/OS is running directly on the LPAR, which wasn't common the last time I looked (a decade ago, more or less).
I suspect that is not an inherent limitation of the dual-ISA design (the HotChips slides mention some sort of bidirectional thread state mapping between arm and z), but just about there not being z/VM release that supports that (building such a thing is probably SMoP, but another question is whether that makes business sense).