Our software update is now concluded. You will need to reset your password to log in. In order to do this, you will have to click "Log in" in the top right corner and then "Forgot your password?".
Welcome to PokéCommunity! Register now and join one of the best fan communities on the 'net to talk Pokémon and more! We are not affiliated with The Pokémon Company or Nintendo.
I've spent about 5 minutes looking for it on new UI and couldn't find it anywhere. Then I switched to old style and found it in 10 seconds. I compared both versions of settings and I have to say that it's missing in the new UI. So the only way to turn pop-up off is switching to one of the older styles and switch it there.
The new UI doesn't have the option to turn off pop up notifications because it doesn't have those. It's only on the old UI that it throws a pop up at you whenever you get a PM