If you are issued a parking ticket on your windscreen, you can make your payment right away. All you need is follow the instructions on the ticket. Paying instantly is recommended because you may have to pay an additional fee if the authorities send the unpaid parking or traffic fines to the rental car company.
Whether you get caught for speeding or committed some other traffic offence while driving a rental car, the rental company will charge you an administrative fee for dealing with the fine. Usually, this fee is charged on your credit card. You will be then notified via email by your rental company about the fine. In the event your credit card is charged a few weeks after you've returned the vehicle, make sure to contact the car rental company immediately to get more information about the charge.
Read more about Driving a Rental Car in the USA.