I would surmise after a cursory glance through the code(s) for both the Spun theme and the 'create a custom page with circles on it' guide that the script to create your custom circles does not return 'true' for is_single, is_home, is_archive, or is_search. In the functions.php page for the Spun theme, one of these conditions must return 'true' to display the navigation bar.
You MIGHT be able to fix this by resetting the post data. In the index.php page in your child theme folder find the statement that inserts the nav and insert wp_reset_postdata(); just before it so that it looks like this:
<?php if ( $custom_circles->post_count > 0 ): ?>
<?php get_template_part( 'content', 'custom-circles' ); ?>
<?php endif; ?>
<strong><?php wp_reset_postdata(); ?></strong>
<?php spun_content_nav( 'nav-below' ); ?>
<?php elseif ( $custom_circles->post_count > 0 ) : ?>
Save the index.php file and refresh your page.
Again, this is just a guess. It is NOT tested. It MIGHT work.
If it does not work, remove that line.