You say it yourself:
I have added some extra information via a Custom HTML module relating to that category that displays in a module position below the page content only for that menu item.
The top menu is a different menu item. Thus, that module is not displayed on it. And all links in that menu item use the same menu item, so what you have is normal.
Why not do it differently ?
Instead of your module, add your text in the description of the category. Then, in all your menus' hikashop options, turn on the "show description" option and you will see the text for that category, regardless on which menu you are.