How do credit card late fees work?

It was probably posted after the close of business time (5:00 pm). Call them to see why and hopefully get that late fee refunded (not likely, though). Always pay the business day BEFORE the payment due date. It used to be that if the due date was on a non-business day, the due date was shifted to the next business day (Monday). But with the advent of online payment capability and the ability to accept payments 24/7, there is no "non-business day".

Contact them about the fact you paid it on the date it was due. If the bank took a day to process your payment, you were a day late according to the credit card company because they did not receive the money on the date you paid it.

Generally you should be paying it a week before the due date, to avoid stuff like this.

There's probably a time of day cutoff.

If you don't pay it before it is due, then it is late and you get charged a late fee. The time that it is due varies, but it's typically in the middle of the day. If you pay on the due date after that time, then it is late, and you get charged a late fee.

The due date is the date that the credit card company has to receive the payment. You need to pay at least one week early to ensure that the payment is received in time.