At the moment the Tesla app only shows a notitfication when the car has already downloaded an update and it is ready to install. In the car you see a yellow icon indicating an update is ready for download if you connect to wifi.
It would be cool if you could create a "Software update X.Y.Z ready for download, connect to wifi to download" as that would enable users to install updates faster. This could be pushed via Pushover API.
Customer support service by UserEcho