Silverturtle Grammar question!!

I was doing the practice writing questions in the silverturtle guide and I came across a question that I am a little confused about.

The problem is number 24 in practice #5:
The people sitting behind me in the theater were talking throughout the film and would not keep their voice down even after being asked to do so.

The error is the “their voice” part. However, I was wondering about the phrase “the people sitting behind me.” I believe the word “sitting” here is used as a present participle, however this sentence is in the past tense. So I was wondering why silverturtle said it is grammatically correct to say “The people sitting behind me in the theater…” as opposed to “The people who sat behind me in the theater…”?

Thanks everyone!

Yes, the people sitting behind me is fine–the participle is a modifier, like “The man selling loose cigarettes on the corner was choked to death by the cops.”