How to automatic update date and time when save custom post type

Using your example link, I just added an IF to check for post_type.

function reset_post_date_wpse_121565($data,$postarr) {
    // var_dump($data,$postarr);  die;// debug
    if($data['post_type'] == 'new_cpt'){
        $data['post_date'] = $data['post_modified'];
        $data['post_date_gmt'] = $data['post_modified_gmt'];
        return $data;
    }    
}
add_filter('wp_insert_post_data','reset_post_date_wpse_121565',99,2);