I've set everything up, but the customer doesn't see a button for changing the payment method.

Two most frequent causes for the absence of the button in customer accounts are:

  1. You have Magento 1.6.x or newer
    Most likely the extension has no payment methods to offer to change to and it doesn't show the button to avoid confusing the customer. Not all payment methods are able to work correctly if the order's payment method is changed. So you have to decide which payment methods to offer by disabling unwanted methods in the extension settings.
  2. You have Magento 1.4.x or 1.5.x
    There is no way to insert the button automatically without changing the template. See Extension peculiarities on older Magento versions

Last modify date: Thursday, October 20, 2016