When I leave my house the Echo Dot is off but when I come home it's playing the last music station I was using.
I've had something similar happen to me and I think I know why. I listen to my favorite talk radio almost everyday. When I ask Alexa to play the station and she acknowledges the station and begins playing. All is good.
There's a few times when Alexa acknowledges the station I stated, but nothing plays. And there's also been times when the station just stops playing midstream with no apparent reason. I think it's actually playing a silent stream. When this happens, the station begins to play again by itself some time afterwards. This time could be a few minutes or hours later.
I believe the reason this happens on occasion is because TuneIn or the station's streaming service stopped working. Alexa never loses the connection and as far as she can tell, she is still playing the station. If I turn on my radio I can still hear the station, so they are still broadcasting. It's just something with their streaming provider that's not working right.
This doesn't happen very often but it could have happened to you. Were you playing a station prior to leaving the house? Maybe your station's streaming provider had a problem and your Echo was silent (although it was playing a silent stream). By the time you returned home, the station is playing correctly again.