That's what I thought. I created the CB Page, menu, then the module, and assigned the module to the template position (Joomla template position) and published it, assigned the menu module to the CB Page and it did not show up. So then I created another menu and module specifically to be used for the CB Pages only then I changed the template for the CB Pages to Flexistrap and chose a position in flexistrap and it did not show up.
Finally to resolve my issue and force a menu on to the CB page I created a tab and field and added in the page links. It would have been a whole lot simpler if I could just add the existing menu across all page assignments though because I have more CB Pages to make and making the menu links for all the pages will be a hassle.