If you've noticed something from a specific user, and they have at least one post, you can flag any of their posts and explain the situation. It's not a big deal on a low-activity site like this, but doing so anyway can keep you anonymous and also give moderators a better starting point.
Occasionally I have noticed a few questions that seem to have gone through that First Post queue without any action, and spotted certain users that also have selected the No Action Needed option in that queue. So following the suggestion in Jamal's answer, I flagged a post by the user who was taking that action. Most of the flags were marked as helpful, but a few recently have been declined.
Moderators should be checking those statistics, but we haven't been actively doing so. The statistics would have revealed the anomaly that you pointed out.
should I stop raising such flags?