CH-47 Startup
I am a former CH-47D IP, and here is an answer.
The author probably did not intend to imply that the shaking or noises were caused by a fuel or hydraulic problem. I think you may be reading that into the story.
Unless the section of the book goes on to further connect the problem with the physical description of a normal aborted startup, he was just describing the events (although I see how you could think they were connected). He was overly descriptive of a normal startup and shutdown and, without stating it, went right into stating the cause of the entirely normal "sudden shutdown". Most likely, the shutdown was initiated because a crewmember spotted a leaking fluid that had yet to be identified. (Yeah, yeah, I know. If a hook doesn’t leak that means it's empty.)
If you want to know why the shaking made it in the book, if it was "normal", read on:
So why would a writer who has possibly ridden on plenty of helicopters, maybe even Chinooks, think that the shaking was notable? Short answer: Big tandem rotors shake the bird a lot during run-up.
Almost everyone who sits on a hook during startup, especially someone who has little experience sitting on tandem rotor helo's during run-up, will notice quite a lot of shaking and noise. Both are completely normal. They are caused by the imbalances that are experienced as the rotors transits through various rpm bands that are experienced only when the rotor is spinning below normal operating speeds.
All full size helicopters’ rotors are only balanced for specific operational ranges. The tandem design just makes startup particularly rough because they have two unbalanced rotors that are displaced in plane of rotation, waterline, blade pitch, and, most notably, arm. The offset main rotor systems create oscillations that interfere with each other.