The demon Zahn takes the souls of mortals, and the contract has the word 'mortal' under the signature line. Since Paige is not mortal or even part mortal, the contract shouldn't have worked.
Back in prehistoric times, Leo told Chris that magic would not exist until humans were around to use it. This doesn't make sense because humans aren't the only beings to be able to use magic. Demons, angels, etc. have existed way before humans did.