Currently this module provides quite different looking tabs than the theme in use. This makes theming more difficult, because the styles the module provides have to be disabled or overridden to maintain a consistent look.

I suggest that the module doesn't provide any default styles and unifies the structure of the tabs with Drupal core. Then the current styles could be provided as an optional style in module settings. Quicktabs is a good reference where the different styles are exposed in the module's settings.