I don't think that is quite right. During the lottery processing, your applications get processed in a random order. So the one you "won" got processed first.
Then, the process goes down through your requested dates, processing those on THAT one application in order, first to last. As soon as one is successful, the system looks up all your other applications and cancels (or Revokes???) them. I was not aware that it would look you up in the Alternate Leader slots, and cancel those, too.
Your scenario sounds more likely.
She also made it sound like a person reviews all of the winning applications and determines if more than one app is part of the same group or trip to decide if one needs to be revoked.