And many of the door latches are/were heat sensitive strips of metal. When the temperature of the water inside the machine reaches a certain point, and after a period of heating up the metal door latch, the metal deforms and the door pops open. Then after the wash, everything cools down, and the metal reforms. There is just enough tension on the metal latch to make it latch closed and just enough deflection after heating to make it spring open.

P.S. Pro-life tip: Don't forget to refill your dishwasher drying port today with Jet Dry/Glisten/Whatever brand you like, it'll stop your dishes from coming out spotty and helps with the dry cycle.