We always did age=number of minutes. Quietness isn't part of it. But they do need to stay in the designated spot (in our house it is a particular spot in the hallway). But an apology (and a demonstrated understanding of why the heck they are there) is required otherwise it's back in for another round (very rare after the first time).

Having said that, sometimes (depending on the situation) we send ours to their bedroom and they can come out "when you are ready to xyz (required behaviour)". This gives them a chance to cool off without the embarrassment of having to back down from whatever the issue was.