How to Disable In-App Ratings Popup on iOS
Straight to the point, apparently the pop-up message isn’t generated by the app itself. I didn’t delve into the technical conditions of what triggers the message, but the phrasing on the settings itself is evident enough that it is Apple’s attempt to collect more feedbacks. iOS App Store is, frankly, not the place I would search for reviews of an app; it’s a glorified distribution system with some added features.
The actual setting to disable the in-app ratings pop-up is in Settings, Apps > App Store, toggle “In-App Ratings & Reviews” on/off.
I doubt this would stop some developers from asking to leave a review on App Store, which, again, is not the best way to advertise your app in my opinion. App Store’s embedded review system is impractical for both readers and writers. For example, lack of version numbers on a review makes it impractical to understand if it is still valid, and lack of more advanced text editor or API support makes it impractical to write one in the first place. I believe there is a greater chance of finding a good review coverage on Google than scrolling through the actual product page that is the App Store’s.