As this seems to have sparked some element of disbelief, let me rephrase some of it more clearly, emphasising why it is less of a concern than you may imagine.
Except for the "crowd"... actors/dancers in this type of production - who aren't trusted as far as you can spit - everybody else involved is an industry professional.
Things that very much separate industry professionals from the consumer are:-
- They do this every day.
If they're not doing a pop promo they'll be doing the next car ad, or a TV show, or a movie.
- They have been doing this long enough that it doesn't impress them.
They really don't care who the talent is. If they're doing the lighting, or the props, or costume, or... anything... that's the job they're concentrating on. They are quite unlikely to even know or care who the principal is today. Tomorrow there will be another one.
- Their reputation is more important than a leak.
Because they do this every day & wish to continue to do it again tomorrow, they simply know the rules.
The next category, then has to be the talent
For a pop promo, though the 'talent' might think they are in charge & the most important person on set; they're in fact not. They are just the one who has to get it right in front of camera today. Another cog in the engine, another spoke in the wheel.
They do, however, get to post anything they like on social media - so if they choose to leak it, they can, with no repercussions.
It's their career.
Featured on the day may be bit-part players - actual professional actors - who should more properly be called day players. They are also industry professionals, like the crew.
They know not to leak things. It's a part of their job, same as above.
...and now we come down to "everyone else"
These are the ones who don't do it every day. Some might, there are people for whom this is a living. They fall under the 'industry professional' category.
But there are others for whom the whole shoot is somehow 'magic'.
Their chance to shine... to be noticed... to meet the stars... to tell all their friends about it on Facebook...
...for those, there's an NDA & people keeping a constant eye on them, because they are not trusted in the slightest by any of the above categories of cast & crew.
...and now back to my previous answer...
Actors/dancers will have all signed an NDA [non-disclosure agreement] on the shoot days.
This would allow legal action to be taken against anyone revealing details of any part of the shoot they were involved in.
For very high profile shoots they would also all have their phones taken off them for the day, so nothing can hit social media.
Musicians & film crew tend not to be given NDAs specifically - but they know how to keep their mouths shut if they want to work again.
They work on 'secret' projects all the time, by definition - nothing they are ever working on at the time is known to the general public.
[Qualification for answer: I'm an long-time recording musician who now works in the film/TV industry.]