Game reviews are hard because people are playing and are usually annoyed, not as annoying as push notifications but both need to be use sparingly.

I find that when we place an ask for review button after there is a reward, bonus or after something fun, they perform better. As an example, after you play a level and possibly have a reward screen on the result, you do a random/progression based bonus per level or some sort of prize chest/box etc.

Popping review dialogs or buttons to ask for reviews after giving them something is a good way to make them not so angry it is there, you can't do after they rate as a reward as that is gaming the system but before you can butter up their perception. You can game it a bit, give them something then ask.

Timing the ask is key, you don't want to do that randomly as it may be after someone just had a bad level.