After you've selected the flights but before payment, scroll to the GENERAL CONDITIONS OF PURCHASE section at the bottom of the page and click on "Fare Rules, Change & Cancellation Policies" and it'll show you any minimum stay requirements for the selected flights. You're right that a round trip ATL-PHX-ATL from Tue-Thu has different fare rules than Thu-Sun, and that it has to do with Saturday. This is also true between ATL and JFK but not, say, SFO and JFK.