As per title: do I need to “unmount” the Drobo 5C I own, and then shut it down, or the function “shutdown” on the Drobo Dashboard in the menu bar in macOS, takes care of it all (unmounting+shutdown) in one operation?
Does the "shutdown" function of the Drobo Dashboard icon in the menu bar, also unmount it correctly?
To answer your question, using Shutdown in Drobo Dashboard > Tools, will completely shutdown the Drobo.
If you are using the power switch on the back of the Drobo, you MUST first eject the Drobo Volume prior to toggle the switch. If you do not first eject the volume you will encounter File System Corruption.