Naturally, the blood must remove the waste as well keep the body temp perfect. The heart being the regulator and your lungs the pump. Taking large easy breathes always slows the work of the heart.
EVERY MD that takes a person's blood pressure MUST have them do some breathing exercises and talk to them until relaxed, OR THE TEST is faked HIGH and nearly worthless.
I would be more worried if a person's heart refused to speed up when working or exercising.