The specific part of the hind-brain mentioned as controlling involuntary actions like blood pressure and salivation is the medulla oblongata. The medulla oblongata, located at the base of the brainstem, regulates vital autonomic functions, including cardiovascular activities like blood pressure and respiratory functions. It also plays a role in coordinating reflexes and involuntary responses, such as salivation. By integrating and processing sensory information, the medulla oblongata helps maintain homeostasis by adjusting these autonomic functions, ensuring the proper functioning of essential physiological processes without conscious control.