I figure that demonstrating cultural competence is about being open and patient enough to empathize with groups of people who differ from you in how they approach and respond to problems, how they act toward you and others and what they consider to be normal and abnormal, relative to yourself and others like you. Even within a single demographic one can see all kinds of differences among these qualities.
I'm sure you can spin this tutoring experience (which is really cool) to express that you work to understand people different than yourself, but also look for answers to this prompt in your clinical volunteering. Pick the one that paints the most stark image of your abilities to navigate diversity.