When assembling the group for the road trip, Prompto is deemed unsuitable to join. He's not part of the official retinue, he doesn't have any extensive formal combat training, and his background check raised some odd questions. (If he's in a relationship with Noctis there's also the diplomatic faux pas of bringing your boyfriend to meet your fiancée)
So Prompto is still in Insomnia when it falls.

Noctis (and Ignis and Gladio) can't get any word on whether Prompto made it out with the rest of the refugees, simply because no one else is looking for him. Prompto has no one else.

Finally at some later point, Noctis finds him, maybe in Lestallum or in the Hunters HQ outpost, just one lost refugee out of thousands, and refuses to let him out of his sight again.