Good question. And the answer is that the demons can think for themselves.(this was covered in the book as a theory of one of our characters) They are seperate entities who are able to enter the body of the zombie because of the departure of soul. So they are able to occupy that space and use the zombie's body to inhabit the physical world.
And to go even a little deeper, the reason this never happened before is because well, in my world, the world of the demon dead, demons are NOT able to posses living humans because two souls or entities can't occupy the same space. If an evil spirit occupied the space left vacant by the departure of a dead persons soul in the "normal" world he would just be stuck stuck there...the person is dead. So....with the soul gone and the corpse reanimated, they can enter the void and take control of the zombie. Get all that?  If anyone has a follow up question feel free to ask.  Thanks