Secondary links depending on child items of primary links.

When secondary links are provided in block form, they do not follow this behavior in any theme.

However, Garland has a secondary links section hard coded into the theme, whereas A3 Atlantis does not. That is why you see the child menus in Garland, but not A3.

You can add this same behavior to A3 with a little work. The code you need is as follows:

<?php if (isset($secondary_links)) { print theme('links', $secondary_links, array('class' =>'menu', 'id' => 'nav2list')) } ?>

It can be inserted anywhere you want the secondary links to be printed. For example, if you want them displayed at the top of the left column, go to line 28 in page.tpl.php and insert it:

<div id="sidebar-left">
  <?php if (isset($secondary_links)) { print theme('links', $secondary_links, array('class' =>'menu', 'id' => 'nav2list')) } ?>
  <?php print $left ?>
</div>

That's the basics, you'll be able to see your child menus now. It looks pretty ugly, though. Better to wrap it up with some divs, like this:

<div id="sidebar-left">
  <?php
    if (isset($secondary_links)) { ?>
      <div class="block" id="block-nav2">
        <h2>Your Heading</h2>
        <div class="content">
          <?php print theme('links', $secondary_links, array('class' =>'menu', 'id' => 'nav2list')) ?>
        </div>
      </div>
    <? }
  ?>
  <?php print $left ?>
</div>

Now you'll get a nice block-style list of your child menus, with a heading of "Your Heading".