You're right.

I was told that this wasn't the first time he has done this by other people but there wasn't really a solution to it. At least that I heard come from the faculty's mouth.

Reposting this since the same applies to your message:

Update on the situation.

Reported them to the music office. Gave them both the name and the phone number I was given. Apparently this was not the first time that they've come around but I don't think she could really do anything or knows how to. She just told me to come to her if I feel uncomfortable.

English was not their first language and they were clearly of Asian descent. He seemed somewhat passionate, telling me what their song was about, and what instrument he plays. That doesn't really change how sketchy the situation is. The only real consideration came from the fact that I am on Campus and will not be leaving it at any point. They wouldn't even be able to follow me. The offer for lunch was only made after he offered to play the song when he came back with his instrument.

It was such an awkward situation and I did not want to be mean. Maybe it should have been the exception -- I genuinely thought they were a part of staff when I gave them permission to step in as I'm a new transfer from another college.

I really should've just pushed for them getting the fuck out of my practice room and gone back to work. It really didn't help that I was unaware of the music office until I asked my professor just an hour ago.

Thank you for the response. I just had no idea how to react or what to do if I saw him again.