Not everyone poops right after eating but it's normal for some people to poop right after or soon after eating and it's usually nothing to worry about.
There are times that I myself will poop within 5 or 15 minutes after eating and other times I don't poop until 1 or 2 hours after eating.
It all depends on the person but it's normal to poop after eating for some people.
Pooping after eating is caused by a normal a normal reaction known as "gastrocolic reflex" which is the bodies normal reaction your body sometimes has when eating food.
When the food you eat hits your stomach, your body releases certain hormones and these hormones tell your colon to contract to move food through your colon and out of your body.
So the result is you poop after eating.