If you let TT e-file an extended Arizona return, it will not check the box 82F to avoid a late filing penalty, apparently, unless you had TT file the simple extension. TT should ask the question in the AZ section if you filed a Federal extension. I believe early in doing the return (I just e-filed both Fed and AZ), I think TT asked if a filed extension, although I don't recall for sure.
I make the mistake if just getting the extension form on line and filing it by mail. It is very simple. But a reminder if you don't do the extension via TT it will not check box 82F so you may get a late filing penalty you have to respond to.
When asked about this in prior years, the solution was to print the form, check the box and mail it. However, my taxes are complicated and I prefer to e-file rather than mail a huge envelope. So, I sometimes get the AZ late filing penalty since the box is not checked.