Dlaczego kod w wywołaniu sukcesu AJAX nie działa?

success to nazwa callback funkcja, a nie promise .

Powinieneś użyć:

$.ajax({
    type: "POST",
    url: "<?php echo site_url('con_product/ins_product'); ?>",
    data: data,
    success: function() {
        alert("Products list is ready to be printed");
        window.open("<?php echo site_url('con_product/print_product'); ?>","_blank");
        window.open("<?php echo site_url('con_product/form_product'); ?>","_self");
    }
});

Lub done obietnica:

$.ajax({
    type: "POST",
    url: "<?php echo site_url('con_product/ins_product'); ?>",
    data: data
}).done(function() {
    alert("Products list is ready to be printed");
    window.open("<?php echo site_url('con_product/print_product'); ?>","_blank");
    window.open("<?php echo site_url('con_product/form_product'); ?>","_self");
});