To refocus on the original question, I do not think you should be worried just yet. Each admissions office at each school has their own process of determining who will receive interviews: some like HBS are very organized and send out all invitations on the same day/minute while others are a lot less rigid and send them out when the candidates full file has been reviewed by the committee. As you do not have spy equipment in each office to see exactly who has touched your application and what discussion might have been held on your candidacy, it is very reasonable to assume that most of these schools have not fully reviewed your application.
Also, from the early interview notification you received, chances are that you will receive at least two, if not more, interview invites.
Onto a more important factor, make sure that you are well prepared for your interviews. In most cases, if you have made it to this stage, your chances of admissions have increased dramatically and the interview is truly the make or break point in this process. Nothing beats practice.
Kimberly Plaga
Senior Admissions Consultant
Manhattan Review