The symptoms being described are caused by activation of the autonomic nervous system. Since part of the anal sphincter complex is controlled by the autonomic nervous system, it can be seen why this occurs.
Specifically, the Sphincter Ani Internus muscle is the part being discussed. Its actions are entirely involuntary. It helps the Sphincter Ani Externus muscle to occlude the anal aperture (hole) and aids in the expulsion of the feces (bowel movement). Parasympathetic fibers from the pelvic segments of the spinal cord innervate (supply) the internal sphincter. It is not innervated by the pudendal nerve, which carries somatic (motor and sensory) fibers that provide the innervation to the external anal sphincter, and is under voluntary control.
The parasympathetic fibers are part of the autonomic nervous system, so in some people, the activation of these fibers during a bowel movement, stimulate other parts of the autonomic system. Usually the part stimulated is the section associated with the "fight or flight" mechanism. So, the salivary glands, bowels, vision, sweating, heart rate, alertness, etc can all be affected to varying degrees in different persons.
Hope that was not too technical to be understood.