Read more tag shows up on EVERY post

I actually never got to add this section to my answer you are referring to. To remove the read more link from the excerpt is quite easy, you just need to compare $count with $excerpt_length. $count will always be between 0 and the value assigned to $excerpt_length. So what we want to do here is to add the read more link in a condition that states that if $count is less than $excerpt_length, we should not display the read more

To put that all in code, you simply need to replace the following section

$excerpt_end = ' <a href="'. esc_url( get_permalink() ) . '">' . '&nbsp;&raquo;&nbsp;' . sprintf(__( 'Read more about: %s &nbsp;&raquo;', 'wpse' ), get_the_title()) . '</a>'; 
$excerpt_more = apply_filters('excerpt_more', ' ' . $excerpt_end); 

//$pos = strrpos($wpse_excerpt, '</');
//if ($pos !== false)
// Inside last HTML tag
//$wpse_excerpt = substr_replace($wpse_excerpt, $excerpt_end, $pos, 0); /* Add read more next to last word */
//else
// After the content
$wpse_excerpt .= $excerpt_more; /*Add read more in new paragraph */

with

if ( $count >= $excerpt_word_count ) {   
     $excerpt_end = ' <a href="'. esc_url( get_permalink() ) . '">' . '&nbsp;&raquo;&nbsp;' . sprintf(__( 'Read more about: %s &nbsp;&raquo;', 'wpse' ), get_the_title()) . '</a>'; 
    $excerpt_more = apply_filters('excerpt_more', ' ' . $excerpt_end); 

    //$pos = strrpos($wpse_excerpt, '</');
    //if ($pos !== false)
    // Inside last HTML tag
    //$wpse_excerpt = substr_replace($wpse_excerpt, $excerpt_end, $pos, 0); /* Add read more next to last word */
    //else
    // After the content
    $wpse_excerpt .= $excerpt_more; /*Add read more in new paragraph */
}