Custom Categories page

I’ve got home.php and categories-3.php, from what I gleaned from the template hierarchy page, if I go to a category, such as http://www.myurl.com/?cat_ID=3, shouldn’t it first look for and use categories-3.php?

For some reason it defaults back to home.php and I’m not sure if there’s another setting I need to change or if this just isn’t how it works.

Thanks for any feedback.