It depends on the cycle for some. Mine one doesn't do a prewash for the 45mins QUICK cycle. But the ECO cycle does follow the normal prewash-then-wash process as described in the video. Hence I normally use the ECO cycle and put the correct amount of powder in both components. However in a hurry I sometimes just use the QUICK cycle and only use the main component as I know there is no point in adding more. The manual explained all this.
I'm fascinated at the number of people on an ostensibly techincal website who don't learn how their equipment works. You've summed up in a few sentences exactly how mine works, but there are dozens of commenters in this thread who appear to be unaware of the basic funcationality of their dishwasher.
All I would add to what you've said is that when my Bosch does include a pre-wash in a cycle, it checks how dirty the water is and only drains the pre-wash water if is dirty. If the dishes haven't caused the water to become dirty, it keeps the same water for the main wash cycle.
Also, I want to expand upon my first paragraph a little: I'm not having a dig at anyone who doesn't understand their dishwasher. I am just venting/observing that the world is filled with all kinds of different people and reminding myself that I shouldn't make assumptions about people as often as I do.
I've had this realisation many times, but it doesn't hurt to have it again. Communicating with people is lot quicker and easier when I remember that.