Some people who eat a significant amount of tuna experience problems with diarrhea because of the high amount of dietary fiber which this particular type of fish contains. Although fiber is certainly good for the body in a number of ways, it can also have an adverse effect on some people in the form of gas, bloating, flatulence, and in some cases diarrhea.
If you have a tuna allergy diarrhea could be one of the symptoms, though chances are it is just the high fiber content. Just make sure that you limit the amount of tuna that you eat on a regular basis if you know that eating it causes you problems. While certain people find that they cannot even eat tuna because their reaction is so severe, other people have no problems at all with it.