Souls grant a species the bonuses of your Player Growth Attribute Poltergeist regardless of whether or not you are currently possessing them.
For example, if you unlock this for one Succubus, all Succubi you own will benefit from the in-battle buffs and sickness resistances associated with the Player Growth Attribute Poltergeist .
Normal Soul Puppets can unlock them from their Creature Status Menu, accessible by clicking a creature's name at various places within the game.
Premium creatures require either purchasing generous amounts of credit or spending LESP Essences within the Player>Rewards>Soul Collection menu.