Of the first three things in the following picture:
#2 is the picture that I posted. It's the "New Sacristy." Since the article says this was the sacristy designed my Michelangelo, it's not #1, which is the "Old Sacristy" designed by Brunelleschi.
So it's either #2 or #3, which is the Chapel of the Princes. As you state, this is the larger one, but it wasn't built until after Michelangelo's death.
This article could have been way more clear, but normally when Michelangelo's famous sculptures are mentioned, the New Sacristy is what is being referred to. I think that's what the article clearly refers to. Whether they're right in that fact is another question.
Thanks for the site plan. Perhaps the author of the article is confused. The New Sacristy by Michelangelo is a very compact space. It has a single small altar against one of the walls, but this can scarcely be described as a "main altar". Nor do I think there's room there to walk behind it. Finally, I think it's highly unlikely that several generations of Medici grandees would have opted for unmarked graves in the tiny sacristy, as opposed to something more befitting their dignity in the Chapel of the Princes, which was completed in 1601.