Does iOS download iOS updates when using a hotspot?
In short, yes. This is how it works:


By default iOS does not allow the download of any single file above 100MB in size using your device's cellular/mobile data connection
When an iOS device is sharing its cellular/mobile data connection as a Personal Hotspot, that hotspot is seen as just another type of internet connection and not as a cellular/mobile data connection
More specifically, that connection will be seen as either a Wi-Fi interface, Bluetooth interface, or USB interface (depending on your personal hotspot settings)
Since the second device (i.e. the one connecting to the personal hotspot) is not seeing it as a cellular/mobile data connection, it can download files larger than the 100MB cap allowed on its own cellular/mobile data connection


There are a range of settings within iOS settings that you can use to manage what (incl. individual apps) have access to your cellular/mobile data connection, but these settings will not recognise a Personal Hotspot as anything other than another internet connection.