The item you noticed on the back of their belt is a device which picks up the sound of the whistle and immediately stops the clock. It eliminates the 1 second delay which is allowed for normal reaction time.
As for the other questions regarding mechanics of the officials...forget about it. Mechanics in the NBA are far from being standardized. Also remember that any organization can decide on the procedures to be used in the games that they sponsor.
Also remember that the NBA is more about entertainment and money then it is about sport. Keeping that in mind will enable you to figure out almost any question in the future regarding professional b-ball in this country.
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