If the new Fiesta stereo is the same as the Focus (which I believe it is) what probably happened is when you turned off the ignition and removed your key the stereo kept playing so you manually turned it off, similarly when you got back in because you manually turned it off it didn't come back on until you pressed the button.
What you will find is that the radio switches itself off only when you open the door. If you let it turn itself off this way it will turn back on next time you start the ignition.
Aha! Thank you. It was blowing a gale so I didn't open the door lol