As mentioned above, it doesn't visually change in front of them, but the effect in their minds is that the face down watch in their hand shows the "normal" time (why would it not?). Then you don't touch the watch anymore, and certainly you never touch the watch after asking them for the number. So in their minds, you caused the time on the watch to change without touching the watch.
Presentation is key here. You want to minimise their memory of you touching the watch, and maximise their memory of them giving you a number and then you "performing the magic" after that point. For example, when they give you the watch, handle it casually. As if the trick hasn't started yet. You're just holding it to maybe to help display it to other people or point out something interesting. Then you can actually place the watch face up on their hands, look in their eyes (so they look at you rather than the watch), and then ask them to put their other hand on top and hold it tight "so you can start the trick". Note you don't say "cover" the watch, which would imply you don't want anyone to see the face, but rather "hold it tight" and it just so happens that people can't see the face. They don't know yet that the time on the watch is relevant anyway. You can even say, as an after thought, "Actually, before I start, I want someone else to cover your hands with theirs - I want there to be no doubt that I never touch the watch."
The second part is emphasising that the magic happens after the number is named. You should spend enough time doing whatever it is that you say is making the time change. Whether it is the spectators imagination, your mind power, whatever. You can pretend to fail and then try harder. All of this is going on when two spectators have enclosed the watch between their hands. This is the image you want them to remember.
If you just did the trick quickly and mechanically, they will "guess" the right method straight away, even if they didn't see you do anything. The magic is created in the presentation.