Rapid Bowel Movements after eating can just be caused by the food you eat which could be high in fiber or you're eating more of a liquid diet.
However sometimes a Rapid Bowel Movement after eating can be caused by some medical conditions such as IBD or "Inflammatory Bowel Disease" which can cause you to have a rapid bowel movement soon after eating.
There are two forms of inflammatory bowel disease which are Crohn's disease and ulcerative colitis and those can both cause the bowel movement after eating.
If your rapid bowel movement continues after eating for a week or more then I would see a doctor to get tested for those diseases.
They can usually be cured which should stop you from having that bowel movement after eating.
The rapid bowel movement after eating can also be caused by "Dumping syndrome" which is also known as rapid gastric emptying because the contents of your stomach empty much too quickly into the small intestine.
So if it's not just because of food you eat then you should see a doctor about the bowel movement to make sure nothing else is going on.