It sounds like the sequel will only be the conclusion of the Aoi Rasen-Jiu Saishuu Kessen (Aoi Spiral Castle's Final Battle) Arc. For whatever reason Shueisha is treating the Jump NEXT chapters as a sequel, akin to 21st Century Boys I suppose. Sasaki even felt the need to specify that the Jump NEXT chapters would be made available in English. It seems to me like a Shaman King situation, rankings could no longer justify serialization, the story was drawing to a close anyway, so they canceled serialization in Jump in favor of serializing the last volume in Jump NEXT.
I think that when compiled the Jump NEXT volume will not be numbered, but simply titled Nurarihyon no Maho: Aoi Rasen-Jiu Saishuu Kessen. Just a guess, but that is what I think they mean when they call it a sequel. It is going to be treated like Shin Prince of Tennis or 21st Century Boys, but since there will only be a single volume, they won't even give it a number. I've never seen a single volume series numbered.
I understand your points for thinking that. But actually, at the point the manga is, the final battle with the final enemy is, in IMHO, the real conclusion to Nurarihyon no Mago manga's plot and, as you said, the end of its final arc, so it should be added to the numbered volumes even if they call them a sequel.
Usually, Mago's volumes have 8/9 chapters. If volumes 22 (July) and 23 (September) are like this, now (whithout the next 3 chapters in Next!), there's only 6 chapters of 20/19 pages left for volume 24 (a volume of only 114 ?). If they add to volume 24 the first chapter of 64 pages + some omakes, it'l fit the 184/192 average number of pages for a tankobon. And then, the other two will be a 128 pages + some omakes (may be something special because it's the last), and it'll fit the 174/184 minimum number of pages I think usually tankobons have.
IMO they call them a
sequel because they're going to be published in a not normal serialization magazine. And I can't figure a manga having its main plot end published separately of the normal volumes but I don't know very much about this world.