I don't think "the Minfilias" were reincarnations, either. She just hopped to the next girl that was to be born. And when Minfilia gave her remaining powers to Ryne I don't think it was even implied to be a rejoining, either. If anything it was Minfilia entrusting whatever made her the "Oracle of Light", her connection to the Light, and dispersing her own aether and finally allowing herself to die properly. She mentions that the other option would be to remove Ryne's Ego and full on body-snatching her, which wouldn't be anything close to a rejoining.