From what I gather, he's an invention of the film. In reality the girls just disposed of the cut-outs and drawings by throwing them into the river. Arthur Wright searched their rooms and found nothing. In the film's continuity he gets spooked by what he sees. It's implied to be the spirit of the Wrights' dead son, which gets foreshadowed by Elsie talking about a guardian angel. Joseph was theirs and he appeared at the right time to prevent the reporter from exposing the girls - so that they could eventually admit the truth years later on their own terms
I'm gonna die of long hair!