To display post tags in order they entered in the backend, use this within the loop where you want to display. Hope this will helps you to display your tag list.
Where, the tag were display in order based on their created term_id.
if ( is_singular() ) :
echo '<div class="my-button-list" id="my-tags-list">';
echo '<ul>';
$ordered_tag_list = wp_get_post_terms(get_the_ID(), 'post_tag', array('orderby' => 'term_id', 'fields' => 'all'));
foreach($ordered_tag_list as $tag) {
echo '<li><a href="' . get_term_link( $tag ) . '">' . esc_html( $tag->name ) . '</a></li>';
}
echo '</ul>';
echo '</div>
endif;