OK, I already found what you need to do to fix it, and I'm sure I'll probably find the code in the php file which outputs the links so they can be fixed too, but I digress.
When you set up the link to a component, it normally gets an ItemId parameter, so the URL looks like this:
http://domain.com/component/option,com_rsads/Itemid,93/The ItemId parameter gives Joomla! the info it needs to display the correct template and modules. When the links within the component framework don't replicate the ItemId parameter in the URL before the task parameter, Joomla! serves up the deafault template and modules assigned to show when the page/component is 'unassigned' (not assigned to anything).
When I click on one of the categories in RSAds, it goes to a URL like
http://domain.com/component/option,com_rsads/task,categories.details/cid,33/Simply grabbing the ItemId param from the first url and pasting it into the second URL before the task param solves the issue. E.g.
http://domain.com/component/option,com_rsads/Itemid,93/task,categories.details/cid,33/So the next question is where to patch the code. I'll give you Karma if you post the answer here before I do.