<?php
function custom_ajax_order_review_refresh_form_commerce_checkout_form_review_alter(&$form, &$form_state) {
  // give the form a custom callback
  $form['commerce_payment']['payment_method']['#ajax']['callback'] = "custom_ajax_order_review_refresh_custom_callback";
  //refresh the current order
  commerce_cart_order_refresh($form_state['order']);
}

function custom_ajax_order_review_refresh_custom_callback(&$form, $form_state) {
  // set the newly selected payment option to the order
  $order_id = $form_state['order']->order_id;
  $order = commerce_order_load($order_id);
  $order->data['payment_method'] = $form['commerce_payment']['payment_method']['#default_value'];

  // load the order and directly save it again to store the new payment option
  $order_wrapper = entity_metadata_wrapper('commerce_order', $order);
  commerce_order_save($order_wrapper->value());

  // define the ajax commands and refresh the targeted fieldsets
  $commands = array();
  $commands[] = ajax_command_replace("#payment-details", render($form['commerce_payment']['payment_details']));
  $commands[] = ajax_command_replace(".view-commerce-cart-summary", render($form['cart_contents']['cart_contents_view']));
  return array('#type' => 'ajax', '#commands' => $commands);
}