For many stomach problems, the recommendation is to lie on your right side. I would say that you are correct, and that the article is incorrect. However, if you find from experience that lying on your left side gives you less heartburn than lying on your right side, then by all means do what makes you feel better.
It is also known as a cascade stomach.It means that the outlet from my stomach is at the same level as the inlet,so if I am not careful with my diet I get an acid reflux into the gulet also called heartburn.
Welcome to the gastroenterology community! I have no idea what a "cup and spill stomach" is. Do you know of the real name for your condition?