For the Now showing add 'cat' => 6
to the query array like so:
$args = array( 'post_type' => 'movies', 'paged'=>$paged ,'cat' => 6);
and for the Coming Soon add 'cat' => 7
so:
$args = array( 'post_type' => 'movies', 'paged'=>$paged ,'cat' => 7);
but from what i can see you got it working:
http://www.moxidesign.com/dev_chad/movie_category/coming-soon/
http://www.moxidesign.com/dev_chad/movie_category/now-showing/