The application fee will only be processed if the company of the building has ProPay set up. The application fee always uses the operating account of the building, regardless of the setting for the item being linked to the property manager's book.
The system allows account items to be linked to specific operating accounts. Using this functionality, the property manager can collect all of their application fee income. Go to the Companies tab and add an operating account item override (clicking the plus button in the Operating Accounts section) for the appropriate application fee item. After the item override has been added, set the operating account of that item to the property manager's operating account. Repeat this step for every company whose application fee income will be collected by the property manager.