I think that both Hanabi and Hinata are in the main family for now. But once a successor is chosen, they will put the seal on either one of them. Hiashi and Hizashi were twins of equal ability, so the only way to distinguish between the two was age. And it also could be when Hinata turned three, that was the year a successor was chosen (Hiashi over Hizashi). That would make sense... perhaps it had nothing to do with Hinata turning three, it just gave Neji a way to remember and describe the date his fate was sealed... literally.