Actually, you are pretty fortunate. My college requires an interview and interviews are always conducted during September. I interviewed with the committee in med September and the committee letter was sent about October 1. The committee assured me that their letter was timely, but I really was concerned about being late in the application process. So July looks really good to me.
Fortunately, I got admitted to multiple schools, so it worked out, but I was really worried for awhile.
It's not uncommon, and anytime before August is pretty early for most pre-med committees. Mine didn't send out our letters until after the 1st week of August. Add in the time it takes for processing by receiving schools and I wasn't complete until mid-August and even early September.
But I wouldn't worry too much. Being complete by early September still puts you in the running for the first wave of interviews for the vast majority of med schools. Use the extra time to fine tune your secondary essays.