Is there a number of reports needed to get a comment deleted? Or is it not automatic?
You may want to check the Statement of Rights and Responsibilities and see if the comment actually needs to be reported.
I believe it increases in moderation down the list.
Spam or scam
Contains hate speech or attacks an individual
Violence, crime, or self-harm
Nudity, pornography, or sexually explicit content
There must be some sort of issue-handling service that rates the reports. Because there were many times that I have reported comments only to realize the page admin could have just removed the comment.
I believe that it's not automatic and that there are a group of employees who moderate these.