I can't comment on your specific template files but the standard Zen page.tpl.php file has this in it:
<?php if ($secondary_menu): ?>
  <nav id="secondary-menu" role="navigation">
  <?php print theme('links__system_secondary_menu', array(
      'links' => $secondary_menu,
      'attributes' => array(
        'class' => array('links', 'inline', 'clearfix'),
      ),
      'heading' => array(
        'text' => $secondary_menu_heading,
        'level' => 'h2',
        'class' => array('element-invisible'),
      ),
    )); ?>
  </nav>
<?php endif; ?>
Which should answer how the menu gets printed to the page. If you want to dig one step deeper, the $secondary_menu variable is set up in template_preprocess_page().
As to why it's the user menu...if you go to admin/structure/menu/settings you should see this:

If you change the secondary link source to something else you should see that reflected in your theme too.