Before this goes into any huge debate, I would say that the definition of mature is all a matter of personal opinion from experience.
For example, I had a 3 gallon up for over a year, and then upgraded to a 70 gallon about 6 months ago. I thought that the 1 year birthday was a good marker for saying that my tank was "mature". However, I have seen even more growth, changes and general differences in look at the 6 month point of my 70 than I ever did in my 30, probably due to halide lighting and better filtration.
If you are looking for an answer because you want to get a specimen that requires a "matrue" tank, I would say that any grazing angel, or any other fish, especially something like a lawnmower blenny would require at least 6 months of maturity, if not longer, to survive. I personally would love a dragonet but I will not risk having a fish die in my tank because I rushed into it; I would say that a fish like that shouldn't be attempted until at least a year after initial setup due to its diet. Like I said, I don't have one and those who do may argue this statement.
I'm sure the list could and will go on and on depending on the fish or coral or anenome etc.
Bottom line is; don't get ANYTHING until you read extensively about it.
Just my 2 cents . . .as they say