Should the one giving urine be present for all steps?

Depends on the type of urine. Usually the answer would be: Absolutely. Especially if it is for a drug screening. You never know what kind of people are taking the urine. They should be there all the way up until the seal is placed over the lid, the cup is placed in the sealed bag, and it is then placed in the box ready to be picked up. There's some weird people out there. You never know what is going on in someone's life and who's life they might like to tamper with.