I actually use this one
I am not 100% sure about yours, but the way I am used to it is by deleting the old command
< ?php wp_list_cats(); ?> and replacing it with the new one
< ?php echo collapsing_category_menu(); ?>
I dont know if the space between the < and the ? matters or not.
According the the authors website on yours, you can use the arguements so the command you would replace the old one with would be
<?php echo collapsing_category_menu collapsing_category_menu ( $root_id = 0, $order_by = 'cat_name', $order_dir = 'ASC', $css_li = 'page_item', $css_li_selected = 'current_page_item', $current_id = '' ); ?>
unfortuntaely I am not as much help on this one as the one I use simply because I have used the other one more.
Also, the end results I am used to seeing are if say you have the category of "accessories" and you have say "jewelry, bonnets and passies" as 3 sub categories under the main category or accessories, it will make it so you have to click on accessories to see the sub categories. I am still used to seeing the main category showing.
For an example, on http://www.aleeya.net/
I have used it so when you click on "books" on the right it shows all the sub categories under books like Andrews, Computers, etc
Silly question, but did you goto your plugins page and activate it too?