It is known that primals are, to some extent, colored by the wishes of their summoners. The primals we always fight are, for instance, summoned almost with the exclusive purpose of territorial defense or expansion. The amalj'aa want Ifrit to help defend their territory, the kobolds want the same of Titan, the ixal want Garuda to crush their enemies, the sahagin want both of Leviathan. Ramuh is, again, a unique case because he was summoned for the purpose of reconciliation, and Shiva, only ever summoned as Ysayle'sSuper Saiyancombat "mode," has no proper agency of her own. Ravana was summoned for the purpose of territorial expansion and is appropriately bloodthirsty, and Bismarck... who knows, all he does is fly around and eat islands... doesn't seem to have much of a personality at all. [King] Thordan has an identical case to Shiva.
(Not sure why the mogglesguard summoned King Moggle, except because they're moogles and wanted to see if they could.)
So, the intention behind the summoning will color the psyche of the primal, but that said there is still a baseline personality for them to draw on. Good King Moggle Mog XII, for instance, has the regal bearing and mannerisms you'd expect out of a king, but is not as benevolent as he'd seem judging on the myth (no matter what they are based on, Primals always come out as a twisted mockery of the summoners' intentions. Given the Ascians are the ones you have to get the ritual from, this is entirely intentional).
It's kind of like how lots of Greek myths paint Zeus with varying levels of morality, but he always has the same backstory (overthrew his father, freed his siblings, and took his place as king of Olympus), personality (a sometimes petty womanizer), and power set (lightning and wind).