At rest, your blood flows at 4 miles per hour. But your body is only about 5.5 feet tall. So if you do some math, you can say that your blood travels from toe to skull once every second (if you talk big blood vessels it is a little bit faster, if you talk small vessels it is way slower).
When you get scared, your heart beats faster which makes your blood flow faster. Up to about twice as fast.
That means it only takes half a second (a little less) for blood from anywhere in your body to get anywhere else if it travels through the big blood vessels.
Then consider that when scared, your adrenaline is starting from your kidney. It enters your blood in the middle of the body so it needs less time to get to the important places.