The HTML of your page is being written synchronously by PHP. If you want to fade in particular chunks of content when they become available, you'll want to deliver the frame of your page, and then use JS and AJAX on the front end to load content at runtime and fade it in.
Edit After JS was Provided
The PHP that you have provided has an extra else statement and unpaired curly braces. Perhaps it is erroring and that is why your JS is not pulling the content properly. However, your basic approach seems sound.
I should note, also, that running include() on user provided data seems like a pretty big security hole.