It's likely that Hunter's adoption was handled as a private affair using an attorney affiliated with the cult which is the behind scenes agent in the film series. This explains why no one seems to have interfered with his adoption by the family. the film series at this juncture has not made it clear as to the details of the Hunter/Katie scenario between when she kidnapped him and when his adoptive family is murdered.
It can be assumed that Katie placed Hunter up for adoption to make it difficult to locate both of them after the authorities found her sister's family murdered. She then comes to retrieve Hunter at a time when it is appropriate to do so and undertake additional sacrifices to the demonic entity worshiped by the cult.
