Barboh, I have the iPhone 6s Plus 128GB when pulling down the notification screen or swiping up from the bottom. The screen will be slightly transparent where I'll see a slight color of the icons from the home page showing through, but it's not really an issue, or extreme as with what you're pointing out.
What I would try where you're seeing something from a youtube website recently visited etc., is to free up some memory. Press twice on the home button and swipe upward to remove what's been visited and stored. Then go to Setting > Safari > Advanced > Website Data and clear that out to 0 bytes.