Looks like an app permission alert. This doesn't fall on Apples "best practices", at the very least you need your apps name in the alert. Matter of fact all your problems would be solved if the developer used the app name in the alert. Its also nice to have a sentence that makes sense....I guess they assume you'd figure out when they said "HomeKit" in iCloud settings they actually mean "Home"....This is from apples developer page...
It should be noted....
"HomeKit" is a software framework used by iOS developers so their companies products work with another companies products. For example, I have an Eve motion sensor that turns on a Phillips smart light. Eve and Philips didn't need to work together to make this happen because all they had to do was incorporate HomeKit. Since its a development tool its not something you can delete from iOS.
The "Home.app" on the other hand is just an app made by Apple to setup and control HomeKit accessories. It used to be a requirement to use the Home app to setup HomeKit accessories. From there you could use other "Home" apps to control your accessories if you preferred. Access to HomeKit (or Home Data) grants an app access to users in the home, accessories, room names, etc etc.
The "Home" toggle in iCloud settings allows the use of automations or remote access. The iCloud data basically allows the Hub to act in place of your iOS device when you aren't home. If Home didn't have access to iCloud the home data would be local to your iOS device.
Anyway, from what you said I'm highly suspicious of that Mi Home app.