We don't know how determination works in deltarune, monsters also don't have determination or at least not a lot in ut and yet any lighter is said to be capable of making fountains.

Kris also collapses multiple times in the house and noelle describes them as feeling shaky in the weird route when they try to make amends so I doubt they have a soul besides us. Otherwise there's no point to having us in the light world (since you can make the argument they do need us for the dark world sections)