I also work in a University and have experience with student workers. In my experience, student workers are eager to please, hesitant to say no, and need a lot of reassurance that they are doing everything correctly. I suspect that the student thinks he was hired by “the library” and thus takes direction from all library workers. ZPG needs to make it clear to him that she is his only supervisor and how he spends his work hours is up to her.
I choose to take the supportive, friendly approach. “I saw that John Smith has been asking you to work on his filing. I appreciate that you are being helpful to the other staff members, but I want to be sure that you have enough work time to complete the tasks I need done. The next time John asks you to work in his projects, feel free to tell him no if you are busy. If he pressures you, tell him you need to run it by me first.” Empower them to say no and reassure them that you will back them up if the coworker reacts badly.
When I got out of the USAF, my first job was at a public library. One of the hardest parts of managing minions and volunteers was learning that everyone poached, and that the minions would do the tasks out of fear, and the volunteers would do what they wanted.
As has been mentioned many times already, I told my minions that they worked for me and to tell whoever wanted them to do something else to clear it through me first. I also told the volunteers the same thing, but they all did what they wanted anyhow.