The menu name itself is always prefixed with ?q=/ttm/... as default and minimum. This is to avoid clashes with other modules. A typical link in a treemenu, for example GreenShoes, would become,
www.mysite.?q=/ttm/menu-greenshoes/node/9
On paging, Taxonomy Treemenu can handle such URL's internally.
A URL such as this will generate page template suggestions such as,
page-ttm page-ttm-menu page-ttm-menu-greenshoes.tpl.php page-ttm-menu-greenshoes-node.tpl.php page-ttm-menu-greenshoes-term.tpl.php
Thus allowing a designer to style individual menus using a handful of templates.
General information about template suggestions.