I got mine in around 10th of August last year, which was later than I had hoped, and mine still went out in the very first batch submitted to programs. I would say no later than 15th or so if you want to have a good chance of being in that first batch. Apparently it is an electronic submission this year, however, so that target may no longer be accurate.
Bottom line is, the correct answer to your question is turn it in as soon as possible. There are definitely large numbers of people screened every year by different schools because there were too many applications turned in before theirs.