Well, as I said, way out of my field, and I haven't read the paper, so about all I can do is try to discuss the language, without regard to the science behind it.
On the one hand, he could be saying that the "heat shock proteins" keep the mutations from happening at all, until the stressor, and then all hell breaks loose. Or, it could be that the mutations are continuing all the time, but not expressing until the stressor. In either case, the outward appearance of the organism will not change until the stressor, but in the latter, the genetic make up of the organism will constantly be changing, whereas in the former, the genetic make up is unchanged until the stressor.
Those who would sacrifice an essential liberty for a temporary security will lose both, and deserve neither. -- Benjamin Franklin
We see monsters where science shows us windmills. -- Phat