It has nothing to do with people or things - 'over' is used for events that happen.
The party had finished = The party was over
The party has finished = The party is over
In fact, both of your sentences about the washing machine are a little strange: it's the wash, rinse and spin 'programme' or 'cycle' which is finished - not the machine itself.
If you talking about the past, you could possibly say 'The washing machine had finished'. By this you mean that it had finished its washing cycle, or that it had finished running.
You cannot use 'over' in this sentence. A lesson can be over, a relationship can be over, a film can be over, a party can be over. But a 'washing machine' can't be over. This makes no sense. If something happens - and has a beginning and an end - then when it has finished, you can say that it 'is over'. A washing machine is not an event, so it cannot be 'over.'