No, this billing system is an accrual based system meaning that cash-based accounting recognizes income when money is received. Accrual-based accounting recognizes income when services are rendered (i.e., accounts are charged). Income (received or not) is matched to an expense (paid or not), resulting in a proper match of revenue.

Therefore payments received are always applied to the total balance owed and never to specific invoice items.
See Also
Inv Report – Invoice Report
What is Accrual Based Accounting vs Cash Based Accounting?