I think a lot of this labeling is rather fluid; there is no central committee giving a final answer.
It is kind of like the color spectrum; going from infrared to ultraviolet — exactly where does red stop and orange begin? Or yellow stop and green begin?
So you can have a heist or a mystery that becomes a horror story, but it isn't a "genre shift" horror if the heist or mystery are not all that prominent, and the audience is never really engaged or intrigued by the heist or mystery.
If those are treated as just an excuse to get some characters into the horror situation, it is not a genre shift.
For example (I'm making this up), we open on six people, three men and three women, that tunneled in to rob a bank, taking a bunch of safety deposit boxes. They get away clean, go to their hideout and start cracking open the boxes, looking for valuables. They find a weird old puzzle box, one guy, Jocko, is weirdly attracted to it, he gets obsessed with solving the puzzle box. He insists, the rest know Jocko is a weirdo that can get violent, so they let him play with the puzzle box and continue cracking the safety deposit boxes. Then Jocko laughs, and opens the puzzle box — And all six criminals are suddenly somewhere else, each in different rooms of a huge, crazy old mansion. We pull back and this mansion is on an island in the middle of nowhere. To avoid cliché, let's say it is beautiful, a paradise, absolutely serene. Heaven on Earth, until we see the waters around it,filled with dead fish.
So, some elements of a crime, some fantasy element, but if I do all the above in the first 12 pages of a script (typically the setup for a catalyst; 1/10th to 1/12th of the script), this is not really a genre shift.
I don't get the audience interested in how they got into the bank. We saw a tunnel. Or whether they will get caught, as the police are never involved.
Heist movies are all about the how, the clever ruses and unexpected genius and trickery, the con games. In Ocean's 11, we wonder why we need a master pickpocket, an electrician, an acrobat, the remote control brothers, etc; but it all comes together.
In my little example, there is a magical transport but we don't get deep into the rules of magic, it is just there so we don't have to explain how we got from the Suburbs to a malevolent mansion on a mystery island with no way to escape.
To be a genre shift, I think you have to provide more of the tropes of the genre: To the audience it has to feel like a mystery unfolding before it becomes horror. A full act:
- Robbery, and criminals escape.
- A detective at the scene of the crime.
- The distraught but senile owner of the puzzle box is terrified.
- The detective, from photographs, discovers some backstory of the puzzle box, teasing the audience into the supernatural horror aspect.
- She is led to a Chinese monk  that tells her about the puzzle box, and uses a ritual to divine it's location; so more supernaturalism.
- She doesn't believe it at first, but then follows up and finds their hideout.
- She arrives just in time to be transported with the criminals.
Seven beats; about 15 pages. Ultimately, supernatural horror aside, maybe the detective is the sole survivor, the criminals die horrible deaths, but she figures out how to re-trap the evil in the puzzle box, and when she does, she is magically returned to the hideout she found, puzzle box in hand. The criminals are nowhere to be found.
So technically, mystery solved! With about 60% of the story a straight-up horror flick between the first act (~30 pages) and the Finale (~15 pages).
I'd recommend this kind of genre-shift as a fun way to pad out an otherwise simple horror concept.
(Edited to correct a minor bug in the plot.)