Auto update publish date of CPT Post if default post custom field value match to cpt post CF Value

Try using hook on update post meta for post update date.
Something like code below, just change the company_title_meta and company_role_meta to your correct meta key.

If something does not work, send a comment and I will try to help you

add_action( 'updated_post_meta', 'on_post_update_after_post_meta', 10, 4 );

function on_post_update_after_post_meta( $meta_id, $post_id, $meta_key, $meta_value )
{
    if ( in_array($meta_key, ['company_title_meta','company_role_meta']) ){
        $time = time();
        $my_post = array(
            'ID'            => $post_id,
            'post_date'     => date( 'Y-m-d H:i:s', $time ),
            'post_date_gmt' => gmdate( 'Y-m-d H:i:s', $time ),
        );
        wp_update_post( $my_post );
    }
}