How to create secondary local tasks or secondary tabs, also called sub tab (second level) menu items.
It was not clear to me why it was necessary to create a MENU_DEFAULT_LOCAL_TASK in every tab level. In order to tell drupal's menu system to show primary and secondary local tasks, there is a need to create a default local task every time. The default local task points to the same page as the parent item but has a path longer by one element.
Parent path:
'admin'
Default primary local task path:
'admin/home'