This phrase has been around very long and has been used in the aviation industry as well as automobile. This is a very good, and more importantly, very easy for anyone to understand way of describing the four cycles of the engine.
Here is an excerpt from an Aviation safety report from 1958:
Air Safety Forum: Reports Presented at the Annual Air Safety Forum of the Air Line Pilots Association
If this was so widely used as to make it into a safety report for the Airline Association in 1958, it must have been in common usage well before that.
I would venture to say the phrase or a similar phrase probably appeared as cars were becoming a household item and mechanics had a need to start explaining how things worked.
Actually, I wouldn't be surprised if the great Nikolaus August Otto, inventor of the four-cycle engine had a similar saying to explain his engine: Saugen, Drücken, Knall, Schlag...