I thought some installation methods did allow for auto updating apps such as root or Aurora Services. Less concerned about that, I'm fine with checking and installing updates, they made it pretty easy. I'm more concerned about if/what data, even if anonymized, is flowing through the Aurora Store. Obviously the get request and the files themselves for downloading, but do/can apps use it as a gateway to send information out? I know that GSF and GMS fulfill functions for apps but I am not sure if the Aurora Play Store does, such as push notifications.Think of Aurora as a proxy: they log into Google so you don't have to (and Google doesn't know what apps you download/use). They send you the generated download link and you install.
The app doesn't do automatic background installs. This is good because you shouldn't always jump on every new release as it comes out - it could mess up your data of it's buggy.