On the note of the discussion of Primals and their influence upon the individual, bear in mind that a Primal's very existence is, at its core, entirely predicated upon belief in the entity in question. Thus, it can easily be extrapolated and understood by the multiple examples of this exact thing happening since Heavensward that if an individual specifically believes themselves to be any particular identity, they will become that entity, provided that all the other catalysts for the summoning of a Primal are present. And because the individual embraces this belief, they most likely will retain full cognizance and will not undergo some form of self-Tempering by embodying a Primal. The only SLIGHT case to the contrary is with that one Kobold and the whole subplot surrounding him and Alisaie before she got souljacked to the First, but, even then, that half-assed Titan summon still partially had some of that kid's cognizance despite the fact that he was clearly mad with grief.
In all the years I've been keeping up with this game, the devil's always in the details for this sort of thing. As hit and miss as the story itself gets from time to time, the worldbuilding has almost consistently been superb with all the subtle details and explanations for things that can be gleaned with just a bit of careful observation and critical thinking. For instance, I already had a fairly decent theory since way back in mid-2.x that the whole "Warrior of Light" thing wasn't exactly all that special and it was more just a title that anyone could attain with enough renown and deeds under their belts – that it wasn't just some literal "Jesus Christ" role like a lot of the vocal portion of the fan community seemed to assume it was. The only way I reasoned this out for myself was through considering the fact that we knew even back then that numerous people could possess the Echo, and that everyone was also aware that there were multiple Warriors of Light at the time of Dalamud falling – all of whom we know were mostly average, if consistently successful, adventurers. And it took until post-5.x for the story to directly address that matter and prove my theory correct. In fact, I dare say it's a bit more surprising that we didn't have MORE NPCs awakened to the Echo from witnessing Dalamud's fall and Bahamut's very brief rampage at the time considering that the spectacle was fairly reminiscent of the Final Days.