Usually when someone experiences diarrhea after eating tomatoes, it is because they have a food allergy. Certain people have food sensitivities though, which are completely different from food allergies. If you are allergic to a certain food, you will find that some of the more common symptoms that present are diarrhea, respiratory problems, hives, gas, and bloating.
Diarrhea after eating a certain food can definitely indicate that the person is allergic to it, though that is not always the case. It is possible that someone who experiences diarrhea after eating tomatoes has eaten them past their expiration date. Those who have not already been checked for food allergies by a doctor will want to do so as soon as possible.