Interesting app, you've done a good job of the web app fitting stylistically with the ios app. I don't quite understand though what you want to happen. For me (iOS) the background html slides behind the header. Can you describe please what you want the behavior to be, do you want the header to mask out the html behind? Possibly its working differently for you than what I'm seeing.
I just looked again and this might be your web header that's misbehaving, that's a fixed header which is possibly not what you wanted. If the html didn't provide the header and instead you let Jasonette do that it might look better, but your web page is a squarespace site so not sure you have that much control. It's still possible to get it to look good though I think, I'm just not sure how you want it to behave. It's hard to describe these things.
You may way to play with layers for your header, since your app is essentially a full screen web app a layer would allow you to place anything anywhere. I also thought that using the navigate url transitions (https://jasonbase.com/things/74L2) looks better? This works better though if you remove your html header - see the example linked.