Based on my experience, it's totally random as of lately, if not by Friday it should be by Monday or in between.
As for the pop-up, again random. I never got the pop-up for TG edition, before it would be like 1 week after it's in the Google Play Store, now it's 2-3 weeks after. I still haven't receive the one for PSS yet and it's in the store like almost a month now.