When you log in to see your application status it will give you the date they actually received it. If you sent it on a tracked delivery and know they got it on the 10th, chances are when you log in it will say they received it on the 10th so you'll be certain that it is from your second application.
When mail arrives at Sydney it is stamped upon arrival in the mail room with the received date, so even though your AOR was later, when someone actually checked your application out, they will still go by the date stamped on your envelope in the mail room as the day they received your application, rather than the later date of your AOR.
Congratulations by the way. This must have been incredibly frustrating for you.