"What if my member makes a payment at the school so his/her card is not charged via autoCollect?"
Simple... Here is what you do:
If they are paying you by credit card through RainMaker Point of Sale, go to Point of Sale and mark the transaction type as Tuition, then process it, it will give you the steps you need to make sure the next payment date is handled properly.
If they gave you a check or cash then search for the student and go to their detail page.
Scroll down to Payment History. At the bottom of all the payments, there is a button "Apply Tuition", click that button and follow the directions.
Hope this helps!