Radio in mine turns on with the key in my pocket. Doesn't matter how long the car has been OFF I don't think. Will it shut itself off after a period of time? Not sure - never had to find out. It's also interesting that if the radio is ON when you shut the car off, the radio will go OFF, but it will turn ON as soon as you start the car up again. At least that's what happens in my two EV's.
2014 EV Coupe 20,000 miles
2014 EV Cabriolet 17,500 miles
Yes, normal. The radio will turn on even if the key isn’t in the ignition. Will play for about 30 minutes then shut off. The modern radio, unless it has a complex amp system, doesn’t run the battery down in that short of time. No worry.
Mine works that way too. Turn the car off, hit the power button on the radio and it'll come on. I've never left it on, so I don't know how long of a timer, if any, there is, but there probably is one.