i don't think amcas is available for the schools to download until july sometime around the 10th. i got secondaries 5 days after amcas was submitted. The last one i got was sometime in early october. All i know is that all of a sudden i had around 17 secondaries to do and now letters of rec. Make sure you have all your letters before you turn in amcas, it will give you comfort
The timeline is as follows. You apply around early June, hopefully on June 1 but most likely a little later like June 3. The applications are not transmitted to the schools until around July 12 or mid July. You then get secondaries late July and all of August.
You will work on most of your secondaries in late July and early August. You typically send in your LORs around the same time you send in your secondary to a school. It is a lot easier if you have a LOR service as so you can just tell them to send it to each school as you get a secondary.
The interview invites start coming in late August, September, and so on. Good luck.