AFAIK,Completed means the judging is done and sent to the AHA. Processed mean inputing the results into the database. I believe Janis Gross pretty much runs the whole show (with help I'm sure) and does all the database work herself.
Mailing of scoresheets is the responsibility of the site organizer.
Here is a reply from Tom Schmidlin, who is on the AHA Governing Committee, on the message I sent him:
The instructions to the different regions were clear, but some of the
organizers either did not read, did not remember, or ignored them. Since we
rely on these volunteers to actually run the competition, we don't want to
give them too much of a smack down when they break the rules.
We'll talk about how to address this in the future, maybe increase the
number of places where we explain things, reminders judging weekend, or
something like that.