The passage you quoted sounds like he was describing a bottom up process, where stimuli are gradually processed by afferent neurons in the nerve signals are sent to your spinal cord, up the brainstem, then spread out to the cerebellum and the rest of your brain. This isn't controversial, and very easy to observe by any neuroscientist when they look at neurons directly. By the sound of it, what he terms emotion is bottom up. As I recall, Damasio makes a distinction between feelings and emotions.
It doesn't say anything about top-down processes, which undoubtedly exist, where signals are sent the opposite direction, through efferent neurons at the very end. Any cognitive psychologist like Damasio believes in top-down processes.
You would be right if he was claiming that all brain processing is bottom up. That would be the thinking of a radical behaviorist probably, who effectively thinks everything is the result of bottom-up processing.