Here’s a basic UI thing that needs to happen: spatially stable navigation.
When I scroll up, something should not appear unless it was just hidden by my scrolling down.
When I hit “back”, I should always be where I just was.
These are, in some ways, the same thing. Scrolling up on a webpage is, quite often, intended as an “undo” for the previous scrolling-down action. When I scroll up, I want to see the last thing that disappeared under the upper fold. I don’t want to see your menu, which wasn’t there before.