Paginated Author.php not using Author.php template

This is not fix for your issue is only an working example of what you can use for the author.php page.

<?php 
 $number   = 10;
 $paged    = (get_query_var('paged')) ? get_query_var('paged') : 1;
 $offset   = ($paged - 1) * $number;
 $users    = get_users();
 $query    = get_users('&offset=".$offset."&number=".$number);
 $total_users = count($users);
 $total_query = count($query);
 $total_pages = intval($total_users / $number) + 1;

 echo "<ul id="users">';

 foreach($query as $q) { ?>

 <li class="user clearfix">
   <div class="user-avatar">
    <?php echo get_avatar( $q->ID, 80 ); ?>  
  </div>
  <div class="user-data">

  <h4 class="user-name">
    <a href="https://wordpress.stackexchange.com/questions/275306/<?php echo get_author_posts_url($q->ID);?>">
      <?php echo get_the_author_meta('display_name', $q->ID);?>
    </a>
  </h4>

     <?php if (get_the_author_meta('description', $q->ID) != '') : ?>
    <p><?php echo get_the_author_meta('description', $q->ID); ?></p>
    <?php endif; ?>

   </div>
  </li>

  <?php } 

  echo '</ul>';

?>

<?php
  if ($total_users > $total_query) {
  echo '<div id="pagination" class="clearfix">';
  echo '<span class="pages">Pages:</span>';
  $current_page = max(1, get_query_var('paged'));
  echo paginate_links(array(
  'base' => get_pagenum_link(1) . '%_%',
  'format' => 'page/%#%/',
  'current' => $current_page,
  'total' => $total_pages,
  'prev_next'    => false,
  'type'         => 'list',
  ));
  echo '</div>';
?>

You will also need to adjust the css classes to match your theme styling