Here’s the basic biology: glucose in the bloodstream above about a U.S. tablespoon is dangerous, possibly even deadly if it gets too high. Dr. Phinney describes it as a “metabolic emergency.” Not only can hyperglycemia cause coma and death, but the excess glucose also causes damage to proteins by glycosylating them—and then you’ve got all those advanced-glycation end-products running around, causing damage of their own.
To deal with the metabolic emergency, the pancreas acts on the elevated serum glucose by secreting insulin from the β-cells in the Islets of Langerhans. The effect of the insulin is to drive the excess glucose from the bloodstream by forcing muscle cells to take and metabolize it, and forcing fat cells to store it, in the form of triglycerides. A chronically high insulin level also creates other problems: raising blood pressure by messing with the nitric oxide balance in the blood vessels, causing inflammation in many areas of the body, and so forth.
So yes, too much blood glucose causes your insulin to go up, and the dip in blood glucose you are seeing after drinking that BPC is caused by an increase in your insulin level.
The point of a well-formulated ketogenic diet is to keep the insulin level as low as possible for as much of the day as possible, so if something you eat spikes your insulin, you are working at cross purposes with yourself.