Something I can't understand in Acquia Marina theme
The Acquia Marina theme is a sub-theme of Fusion core. $primary_links_tree is defined in the template file of that theme, in the fusion_core_preprocess_page(), which the preprocess function that is called before page.tpl.php is used to output a page. Starting from line 80, you find the following code:

$vars['primary_links_tree'] = '';
if ($vars['primary_links']) {
  if (theme_get_setting('primary_menu_dropdown') == 1) {
    // Check for menu internationalization
    if (module_exists('i18nmenu')) {
      $vars['primary_links_tree'] = i18nmenu_translated_tree(variable_get('menu_primary_links_source', 'primary-links'));
    }
    else {
      $vars['primary_links_tree'] = menu_tree(variable_get('menu_primary_links_source', 'primary-links'));
    }
    $vars['primary_links_tree'] = preg_replace('/&lt;ul class="menu/i', '&lt;ul class="menu sf-menu', $vars['primary_links_tree'], 1);
  }
  // ...
}