In the above commenter's case it was a university VPN, meaning the servers were run by the university on the university's private network. That means the university can monitor everything you do on it. The professor's mistake is that they heard ads from commercial providers saying VPNs make you anonymous and assumed the university VPN was the same thing. Commercial providers have servers set up in a variety of locations so you can make your traffic appear to be coming from somewhere else, and most at least claim not to log any traffic and will present independent audits as proof. If the professor had used a commercial VPN provider instead then the university would not have known what they were up to. It is still possible for the websites you visit to deanonymize you through the use of trackers, cookies, fingerprinting, etc. and there's no real guarantee that the VPN providers are being truthful as some have been caught giving logs they claim not to keep to law enforcement agencies.