When you submit, your application get's put into an ordered pile. As each application's list of transcripts are completed, they get pulled and "audited" by somebody there at the AAMC. Once they are done making corrections to your AMCAS coursework using your official tanscripts, the application is certified and then sent out to schools.
Now, the earlier you hit SUBMIT, the higher in the pile your application will be. Those who submit early in this process get processed ("audited") quickly, say in a week or two or maybe even in days. Those who are being processed in September may be in a 1.5-2 month wait. So you see, then longer you wait to hit SUBMIT, the longer out your primary application gets to the schools.
Since you submitted in June, you have nothing to worry about as long as all your transcripts arrive to the AAMC soon. You'll be processed ("audited"), your primary application will be submitted to the schools, and you'll be one of the first ones looked at.
If you were me last year, you would have hit SUBMIT in mid September, you'll have to wait 6 weeks for them to certify ("audit") your application, and be stuck filling out secondaries in November, stressing out over Christmas break, and pulling your hair out in January, early February with no interviews.
