@norseman no the door opening was on a bus, not car, in early years did not see diesel automatics with cars, although 1980 USA style school bus I drove in Algeria was fully automatic, but British buses were semi-automatic. The DAF belt drive was also used with Volvo, Ford and Honda, although moved to stainless steel belt not rubber, but same idea, these boxes did not seem to kick down in the same way as the epicyclic gear boxes. Large engine cars only used 2 gears the third was only for towing, and the way the boxes worked resulted in needing the read the manual, the Morris Mariana from memory you could manually put in low, as braking and it would only change down once road speed low enough, however this was not the case with the Mini automatic, doing same with that car would likely wreck the engine, plus free wheel on first gear.
I have driven faulty and poorly set up automatics, and have stripped one and replaced the clutch plates in a Rover 3500 after it was towed, some automatics had two oil pumps and could be push started, others towing them would wreak the box due to no lubrication as no oil pump on output shaft.
Putting on a recovery vehicle in Park could also wreak the box.
But today with 8 speed boxes the way the automatic drives is very different from years ago. I drive a manual diesel and to keep revs low enough so turbo not running so does well with miles per gallon one is playing tunes on the gear box changing gear many times driving in Welsh hills, the automatic in the Jag means we are unaware when the gear changes, when we first got it I tried working out what gear I was in, but could not keep count, never tried using paddles. The whole idea is it does it all for you.
So early automatics used more fuel than the manual, but today's automatic uses less fuel to manual version, things have moved on. But the big thing I have realised they are not all the same, and the only option is to read the book on the version you have, in the main yes engine will rev up as you accelerate, but the old idea of kick down has in the main gone, you don't need to press the throttle rapid any more for it to work, the system is far better at working out what engine speed is required to get acceleration and yes I know with the 8 speed it does some times change two speeds at a time, so there is no common answer to the question.