Hello!
Sorry about the delay, I am travelling overseas.
When configuring categories with this module, the link to the category will open a standard Joomla! page of a category, with links to the underlined articles. In order for making sure it appears the way you want it when you click on a category in the module, create a menu item of the chosen category and set it the way you want it. From that point on, clicking on a category from Latest News Enhanced will show that menu item (that menu item needs to be published but if you don't want it to show, add it to a menu called from a module that you will not publish).
I hope this makes sense, let me know...