2 of 2 replaced http://meta.stackexchange.com/ with https://meta.stackexchange.com/

I've run into this too and asked about the threshold for these messages before being pointed at this question.

These messages are about how the SE platform operates; they're about voting, commenting, and accepting answers, not about anything site-specific. So once you've learned those things on one site you don't need to relearn them on another. Yet, according to an answer there and comments here, you'll get these messages until you reach 2000 rep. That's way too high for your second (or later) time through.

While it would be a lower threshold than what we have now, which requires you to get to 2000 somewhere, I propose that the granting of an association bonus should remove these reminders. By then you've gained 200 reputation on one site, which isn't as much as 2000 but also doesn't mean you just walked in off the street (probably -- and if you did and got lucky with a popular post, other users will likely tell you what you're doing wrong).

An alternative would be to check for 2000 on any associated site (not in real time; this could be cached). That's more work but preserves the "it takes 2000 rep to really learn the ropes" idea if that's important.

I suggest testing the association-bonus approach.