Once you are verified, schools get your app from amcas within a matter of days. However, you must realize that many admissions offices are still putting the final touches on last year's cycle, and so it will likely be the first week of July until you start seeing secondaries. Some may send them out automatically, others may screen, and selectively give out secondaries only to those candidates who seem competitive. If I were you, I would rank your top 5 choices (based on how likely you are to gain an interview, and how bad you want to go), and pre-write those secondaries, using last year's prompts. That way when you get your secondary, you can turn it in ASAP.