3) A Commander popped by a Side may have any rank less than or equal to that of the Ruler of the Side. This is randomly determined.
The other option is that it is determined by location. Caesar wasn't popped in the capital, so he is Noble rather than Royal.
I was just re-reading Book 1 in physical form, and the printed glossary answers this. The definition of "Noble" is
"A Commander unit popped to a royal side, in a city other than the capital."
Sorry to beat a dead horse, since Raph among others is already there, but we're (some of us) trying to make this more complicated than it is.
Royal isn't in the glossary, but, if analogous, must mean "a Commander unit popped to a royal side, in the capital."
Also of interest is the glossary definition of "Overlord": "A ruler with no Royal or Noble lineage." Unless Rob's own understanding has moved on, that kind of answers the royalty-nobility-not question about the Firebaughs, and especially Overlord Firebaugh: they're not, and he's not (which kills one of my own theories).