I have my wife and 4 kids on my HHA but only 1 of my kids was ever sent a card and they had all flown the same at that time.
Mrs T has now flown a bit more but timings mean she has never left Blue level but will do so after her next trip which will take her to Bronze.
She has never had a card but guess/hope hitting Bronze will trigger one.

That said I hit Gold back in December and still have not had a card...