USC specifically, I paid the fee right after I submitted my application. As for secondaries, its secondary will come if you are selected to interview (you bring your answers to the secondaries/other papers and turn them in on the day of your interview).
For other schools, usually you pay the fee right after you submit your primary app, if they don't have any secondaries. If they do, then those secondaries will be on a separate portal and you answer those questions/pay the fee through that separate portal-- LLU, Western, ASDOH, MWU AZ, LECOM are the ones I applied to that had this. You check your status with these portals too, not AADSAS. Boston, Tufts, UoP, and UCLA had an online website where it was only to pay the fee, and nothing else.
For anyone:
I applied to a range of schools (about 12), got 8 II, only attended 4 (the SoCal ones) and was accepted to all 4- UCLA, USC, Western, & LLU. Let me know if you have any specific questions about these schools!