I know a lot of us got completely hooked, lined, and sunk upon the word 'alternate,' so to help myself out I decided to go back listen to what all Masuda said.
He said that Ultra Sun and Moon "features an alternate story taking place in the world of Pokémon Sun and Pokémon Moon." This means that this upcoming game takes place within the preceding game. The one thing I gathered from this is that the story of Ultra Sun and Moon is not a retelling of Sun & Moon's story. Considering the games' title and the content within Sun and Moon, my guess is Ultra Sun and Moon will take place in the alternate universe the player can venture into in Sun and Moon through the Ultra Wormhole. This makes sense via a number of reasons:
1. We already know the Alternate World exists, and most of us have likely already been to it.
2. The Alternate World features a completely different Cosmog, separate from Nebby, which explains the existence of another Solgaleo/Lunala.
3. The Ultra Wormhole leading to the Alternate World has never been expanded on.
4. The concept of alternate universes had already been posited in ORAS.
5. Necrozma ain't done **** yet.
Given all of this, however, there is no telling where this 'alternate story' will take place before, after, or during the events of Sun and Moon. For that, we will most definitely have to wait out the coming months for more information.