Apologies for the delayed response. Happy to answer your questions!
The Item Quantity fields are actually handled by QuickBooks. You create an invoice with Inventory Items, hit save, and the Record syncs over to QuickBooks. At this point, QuickBooks calculates the Quantity on Hand and adjusts accordingly - which then syncs back into Method.
The whole process takes only seconds, so its difficult to see how much is going on behind the scenes when you hit that little save button.