If you purposefully shutdown a host then its not considered a HA event, If you were to press and hold the power button for a few seconds that would be treated as a host failure by HA. It sounds like youre planning on shutting everything down gracefully and simply want your VMs to power back up in a certain order?
If that is the case then see the following KB: Edit Virtual Machine Startup and Shutdown Settings
However note that
The Virtual Machine Startup and Shutdown (automatic startup) setting is disabled for all virtual machines residing on hosts that are in a vSphere HA cluster. Automatic startup is not supported with vSphere HA.
No, I'm not talking about graceful shutdown. During my test, I physically pulled out power cables from the servers, to simulate total blackout event.
Is that considered an HA event? Should "Orchestrated Restart" logic apply to such case?
Yes, in that case it's considered a failed host by HA. After a short while it will follow whatever restart rules you have configured for HA protected VMs
Then what can be the reason that it didn't occur? I've set up the VM/Host Rules as described in the guides, but the order in which VMs were launched still remained random.
Is that a known issue?
Should this functionality work when all hosts are powered on at the same time and there's no vCenter present?