Proximity is the issue. If the watch or bracelet wrist is very physically close to the detector, it will set it off.

You're supposed to the watch/bracelet, but you do have to hold your wrist close to your body. You kind of want to hold your hands in front of your body as if you're about to grab one of your wrists with your other hand.

Watches and other jewelry are basically right at the cutoff of detection. They want to detect small knives but not earrings.

This is all absolutely tribal airport knowledge. I had been traveling for work for years, taken hundreds of flights, but I only found this out when my partner tried to go through a metal detector with a semi-permanent bracelet that requires a small screwdriver to take off, and the TSA person mercifully told her exactly how to pose as she walked through the detector.