Admittedly, they didn't "used to be" Solars until they Exalt. Exaltation isn't tied to the soul. For the Dragon-blooded, it's tied to the body, and there's nothing past-lifey about it. For Celestial Exalts (like you guys), mortals with heroic destinies and outlooks just attract "shards" of essence which contain the Exaltation (and, sometimes, past-life memories). Who you were in the past has nothing to do with it.

ITS COMPLICATED.

(Also, the setting isn't really all that medieval. >_>)