We love Joomla, but sometimes things can be confusing. One of those things is when module links are linking to Home page (front-page article section) and in the component section the linked article is opened, but with all modules from Home page.
Ok, the problem here is caused from the lack of a menu item for this exact Joomla article. This is because Joomla is based on menu items. In order to have a page, you need to have a menu item for it. Once you have a menu you can assign modules to this menu item and extend the page however you like.