I've always turned the engine on before using the slime compressor, cars or bikes. I think I've bought the first compressor about 6 years ago after moving into this particular house (bought more compressors since to have one with each car/bike), and since I have a half miles crushed rock down-hill driveway, I really do need these pumps occasionally. I guess I never thought about it very much, just wanted to be sure I could still drive away after the tire pump.... and I have not had a pump fail sop far either.
So far I did not need to use the compressor for my FJR....but I'm sure I jinxed it now!
The pump manufacturer may have said this as a legal CYA (Cover Your ***) so some slope headed knuckle dragger doesn't start this car in the garage to fill his 4 flat tires with the doors closed.