No evidence the author uses this principle, because we’re not told the Typhlodromus population surges “just prior” to a surge in the cyclamen population. The Typhlodromus population might surge just after a surge in the cyclamen population.

Although the author discusses greenhouse experiments and field observations that support the claim that Typhlodromus mites can effectively control cyclamen mites, this doesn’t imply that she thinks these kinds of experiments and observations are “fundamental” to long-term predatory control of agricultural pests. They might add evidence for the belief that sometimes predators can control pests long-term, but there’s no reason we’d have to do these experiments or make these observations in the field in order for the predators to actually keep pests in control.

No evidence the author uses this principle, because the author doesn’t suggest that it is important for the cyclamen population to survive in times of low crop productivity. What is important is for the predatory Typhlodromus to be able to survive in times of low crop productivity so that when the prey population surges again, the predators are still around.

It would make sense for the prey population to be vulnerable only to pesticides that the predator population is not vulnerable to, so that when we use pesticides against the prey we don’t kill the predators. But we have no reason to think the author believes the predator population should be vulnerable to only the pesticides the prey population is also vulnerable. The author would want a difference in what pesticides the predators and prey are vulnerable to.