GE Capital GE Capital Retail Bank You will be penalized for making your payment too early and not on the exact due date.... Internet, Internet

After finally reaching someone in the U.S. (not India), the customer service rep completely understood the situation and refunded all late fees and corrected our account. 

Payments made before the billing date are credited to the current payment period. That is standard with all credit card accounts.

This is how all Credit Cards(Open Ended Accounts) work.  By law they can not apply payments to "future" payments, they can only apply any payment above the minimum to the principal balance.  Just like any charge you make is posted in the current period, any payment you make is also applied in the period it was received.

With a due date of 12/9, most likely the period "closing" date was around 17th-18th of the previous month(give or take a couple days). 

However, they will never send out the next month's statement before the period closes. So you would have received the statement(e-statement or paper) around the 19th.  At that time you would have seen that the payment was posted to the previous month and you still were required to make a minimum payment. 

Or let me guess you are a person who thinks that "statements" are a waste of time and you shouldn't have to review them.