Re: Samsung Trio Stealth 43BMID speaker won't turn off when headphones are plugged in.
Welcome to Android Central! It may be a silly question, but still worth asking--are you certain the headphone plug is pushed in all the way? You should hear and/or feel it click into place. A plug that is not in all the way might lead to sound playing over both.
If it is in all the way and this is still occurring, then check to see if there is any debris in the jack, like lint. Use a damp toothpick to root around, or a can of compressed air to blow it out.
If the jack is clean, then it is most likely faulty hardware or firmware (which would not be too surprising with a budget/off-brand device).