Most writers edit and correct and proofread as they go along.
But in a tutoring session, we look at higher-order concerns first. But when the paper is in its final form, then working on correctness is a vital part of what we help writers do. But we don't proofread, exactly, though these sessions work very much like slowed-down proofing. Instead, we do what's called an error analysis. Here two tutors role-play an error analysis session.