Once the medical schools receive your information from AMCAS/AACOMAS they will respond in a variety of ways. Many schools will ask every applicant to complete a supplemental application, whereas some will do an initial screening and provide secondary applications selectively. The majority of schools make their supplemental applications available on-line. While some will ask you to complete their “secondary” as soon as they are aware you are a candidate, others will not make it available to you until they have received your verified application. It is definitely to your advantage to submit each secondary application promptly, ideally within two weeks of receiving it. Be sure to complete the supplemental application with as much care and thought as you did the primary application. The admissions readers are often dismayed at the difference in the quality of writing between the initial personal statement and the supplemental essays!
If you have neither accessed on-line nor received a secondary from a school within three weeks of the time your application was verified by AMCAS or AACOMAS, you may want to contact the admissions office to insure that your application information has arrived safely and is being processed. Take a look at their website first, however, to see if there is any indication of the status of your file or their screening practices. Certain schools - several within the University of California system, for example - take their time reviewing candidates before deciding whether or not to send out a supplemental application. Just keep in mind that is your responsibility to insure that your file is complete at each medical school.