Update the permalink after the term is assigned

function pm_regenerate_custom_permalinks($post_id) {
    global $permalink_manager_uris;

    if(!empty($permalink_manager_uris)) {
        $default_uri = Permalink_Manager_URI_Functions_Post::get_default_post_uri($post_id);

        if($default_uri) {
            if(!empty($_POST['custom_uri'])) {
                $_POST['custom_uri'] = $default_uri;;
            }

            $permalink_manager_uris[$post_id] = $default_uri;
            update_option('permalink-manager-uris', $permalink_manager_uris);
        }
    }
}

function pm_update_post_terms($object_id, $terms, $tt_ids, $taxonomy) {
    // Trigger only for selected taxonomies
    if(!in_array($taxonomy, array('product_cat'))) { return; }

    // Trigger only for selected post types
    $post = get_post($object_id);
    if(!empty($post->post_type) && !in_array($post->post_type, array('product'))) { return; }

    pm_regenerate_custom_permalinks($object_id);
}
add_action('set_object_terms', 'pm_update_post_terms', 9, 4);