"Always changing, the future is" -Yoda
So the kids are sort of imaginary, sort of demonic pieces, and a lot of reality being changed. And if reality gets changed and you never existed yet are reincarnated into some other family's kid, you might end up with slightly different set of powers. It's okay.
Billy and Tommy have the souls of Billy and Tommy blended into them. But biologically speaking, Billy is the son of Mr and Mrs Kaplan and Tommy is the son of.... at least someone named Shepard