Amex Credit Card Complaint

Amex Credit card department,

Payoff process Florida

I failed to notice for a few months that my American Express card had raised my interest rate on new purchases. Therefore, I have been making payments in excess of my minimum payment requirements in an attempt to pay off this higher interest balance. However, I have discovered that my the entire portion of my payment up to the minimum amount due is only applied to my lower interest rate balance. And that only the amount of my payment over the minimum amount due is applied to the higher rate balance. Is this disportionate application of my payment legal?