Sometimes they watch you pee when you go for a drug test but not always. Watching you pee when you go for a urine drug test is called a direct observation drug test. For probation, court ordered and child custody drug testing then yes they usually watch you pee.
For DOT regulated drug testing in some situations the test is direct observed, learn more: https://www.nationaldrugscreening.com/blogs/what-are-the-dots-direct-observation-procedures/
We see drug testing in prisons and in sporting situations where they watch you pee when you go for a drug test.
For normal workplace drug testing with no suspicion of cheating, typically they would not watch you pee for a drug test.
