That makes no sense. The movie is not canon to the show. We don't need evidence that SM anime is in the same universe.
SM is in the same universe as the previous. There is nothing to prove otherwise. Ash's mom is the from the original series. There is no denying this. Alternate universe do not exist in pokemon tv show.
No. Manga is not canon and neither is the movies. There is no hint of SM being in a alternate universe. Mirror world is not another universe. It is merely a reflection of the real world.
Maybe in most other anime like Dragon Ball Z, movies aren't canon to the anime, but the Pok?mon Anime is different as they generally ARE considered canon unless stated otherwise. Case in point, the events of Movie 2 were explicitly referenced in the Whirl Islands Arc where Ash and James both recognized a Lugia and explicitly mentioned that had previously encountered one during the Orange Islands, which even Dogasu verified as occurring in the Japanese version. And let's not forget the first movie, which was even given a few nods before it aired in the main anime (and actually given a prologue calling back to those events in the anime, which to be fair was mostly the fault of Porygon but still), or how Drew's Hometown is the exact same location as the one as Movie 7, or how Movie 10 had Dawn getting a Lunar Wing in the movie which later reappeared in Sleepless in Pre-Battle (and by extension, Movies 11 and 12 are canon due to those two being directly tied to Movie 10). In fact, if the characters make any indication of having encountered a Legendary before that was only in the movies especially if they have no indication of ever having encountered them in the anime before, chances are the films are canon.
To sum all of that up and get straight to the point of the topic, unless we get direct indication that this movie is not meant to be canon to the anime, whether SM or the whole anime, we have to assume that SM is indeed tied to M20, and thus that if M20 is an alternate universe, then SM is one by proxy. Remember, the Pok?mon Anime is not like other anime, it doesn't rely on the manga and thus doesn't have to worry about overtaking it (hence, technically, Pok?mon has no filler episodes unlike with, say, the Dragon Ball anime, where filler's a necessary evil to avoid overtaking the anime, with the exception of Super where roles are reversed), and as noted with the examples above, the movies if anything actually ARE canon to the anime, and since they are canon, that means if Movie 20 is a parallel universe, that automatically makes SM a parallel universe by proxy. And again, that promo manga, which as you know, was made specifically to tie in SM to the movie, and thus is required to be canon to even work, strongly suggests that M20 does indeed occur within SM, and thus means SM is most likely a parallel universe. Heck, technically, it's not even the first time the Pok?mon franchise has hinted at parallel universes, as the Delta Episode hinted that ORAS and XY took place in a parallel universe from Generations I-V, so don't think for a second that the anime hasn't done something similar with SM and especially M20. And for the record, since there's little indication that the Delta Episode happened in the anime timeframe, we can't say the anime adhered to alternate universes prior to SM/M20, meaning XY most likely is still part of the prior anime.
So far as the mirror universe, again, the definition of an alternate universe is a universe that is not the same as your universe. A mirror universe is not the same as your universe, just being side by side, with it and no actual interactions unless you get warped there by accident. In other words, going by the definition that it's not the same as your universe, it's by definition an alternate universe, no ifs, ands, or buts.