Yes a dishwasher machine does turn off automatically after it's done washing the dishes and rinsing the dishes.
The dishwasher will automatically go through a few different cycles and the first cycle is washing, then the next cycle is rinsing the dishes and then finally the heating element comes on in the dishwasher to dry the dishes.
Then after that is done the dishwasher shuts off automatically and if the dishwasher does not shut off automatically then something is wrong with the controls.
A dishwasher takes between 1 hour to 2 hours from start to finish depending on the size of dishwasher.
It's fully automatic and you can turn the dishwasher on and allow it to go through the cycles but don't leave the house or go to sleep with the dishwasher on because I have had one flood my kitchen when gone as the water level switch got stuck and did not shut the water off.
That's rare that it will happen but it can.
After your dishwasher is done cleaning the dishes and it's finished it's dish washing cycle and has rinsed the dishes and has shut off it is a good idea to open the door of the dishwasher and allow the dishwasher to air out.
Allowing air into the dishwasher helps prevent the dishwasher from smelling and growing mold in the dishwasher.
I always leave my dishwasher door open for a couple hours after I'm done washing the dishes in the dishwasher and it has helped keep my dishwasher from getting mold buildup and keeps the dishwasher from smelling.
You don't want to leave the dishwasher door open all the time but just when you get done washing the dishes and for a few hours to allow it to air out.
It just helps prevent the dishwasher from growing mold and helps the water in the dishwasher dry out and keeps your dishwasher smelling better.
You don't have to leave your dishwasher door open if you don't want too but it's a good idea to do so.