Mine was doing the same thing the first summer I owned.
I store my TT at my in-laws. First few times I went over there and would walk out to the trailer, my stereo would be playing. 1St time i thought it just somehow got turned on. Same as you, I shut it off and next time it would be on again.
I found out that somehow the timer/alarm was set to go off at a certain time. I simply shut off that feature and it hasn't come back on since.
if you have the manual for the stereo, it should tell you hoe to disable the timer/alarm.