Why the link of menu item is not highlighted / black / active ?
The short answer is: because it shouldn't. The link is highlighted using "active" class added to the link by the l() function when current path and link path are equal. It is not controlled by the menu system and it's meaning is "the link to current page" and not "this menu item is active". But there is a class "active-trail" that is assigned to all links and menu items of current active trail. So, adjust your theme to highlight links with this class to let your visitors know where they are. For example: 
a.active-trail {
  color: red;
}
The module doesn't work with the menu generated by Taxonomy Menu module. How to fix that?
If your taxonomy menu was generated using some non-standard paths go to the node type settings and for the "Term path" setting select "Ask Taxonomy Menu". If this doesn't help, read the answer for the next question below.
The module doesn't work. What's next?
The most common reason is wrong term path configuration. First of all, check that the real path of your menu items and term path settings in Taxonomy Menu Trails match. To get the real path of the menu item go to the menu editor at admin/structure/menu path of your website, click on "List links" and edit the menu item you want to see in expanded menu on the node page. The field "Path" will show you the real path. Now go to the node type settings and adjust Taxonomy Menu Trails settings according to this real path: choose appropriate term path type and enter path patterns if needed.