If you read the documentation it should be clear to you that pages in the menu are not physical .aspx pages and pages are not added to the menu by creating them in Visual Studio. Pages in the menu are virtual and are all served by /Default.aspx.
If you want to create a page with a custom feature on it you need to implement the feature as indicated in the documentation so it can plug into a page in the content system.
Hope it helps,
Joe