Hi,
No, you don't want to remove that associated module. If you remove it, when you click on a category, you won't see any products anymore as it's that associated module's role to display them. And that's why the system regenerate them automatically as otherwise, your category listing would be useless.
If you don't want the products to display when they are not directly linked to the current category, but only to the child categories of the current category, what you need to do is to change the "sub element filter" option of that associated module to "direct sub elements".
The enable state of the module via the joomla module manager is not taken into account by the menu as the enable state of the modules manager dictates whether the module will be displayed by the template or not, while the enable status of the module in the "associated modules" option of a menu dictates whether it will be displayed by the menu or not, and so these are two different things.