The colour of ones hair tend to change as one grows up. It could be perfectly believeable for Tidus to have brownish hair as a boy, and blond hair when he was an adult.

To be honest, I don't think the creators of the game meant for him to have dyed hair, I believe they just thought he looked cuter with dark roots and dark eyebrows (those eyebrows could be a giveaway, though - blond men tend to have blond eyebrows as well).