Ok, so this is a simple one. The basic rule is, that you will always see the exact component that you are viewing. In case you are previewing the template, you will only see it, and all fixed content linked to it. In case you are using a component include with the dynamic selection of "include template's content component" you will see only the template with a placeholder for components. 

In this case, if you want to preview how your default landing page (e.g. the home site) looks, you will need to preview that exact component.