Exclude category from Tag Template

Have you tried using a normal loop in your tag template like this

<?php while ( have_posts() ) : the_post() ?>
    //add content code or template
<?php endwhile; ?>

And then using the pre_get_posts filter like this

function exclude_category( $query ) {
    if ( $query->is_tag() && $query->is_main_query() ) {
        $query->set( 'cat', '-433' );
    }
}
add_action( 'pre_get_posts', 'exclude_category' );