success's function is called upon the get request receiving a valid response as @harsh pointed out. Thus it will occur after the get request. I believe something similar to the following would do as you request though I haven't tested it:
<script type="text/javascript">
$(function () {
$("#form").on('submit', function () {
var $form = $(this);
$.ajax({
type: 'GET',
url: 'index.php?route=payment/bank_transfer/confirm',
data: $form.serialize(),
async: 'false',
success: function () {
$.ajax({
type: 'GET',
url: 'https://example.com/payment.php',
data: $form.serialize(),
});
}
});
});
});
</script>