No, phobia's aren't dictated genetically. It can, however, start very early. Even before our memories start registering (as such it can seem like we were born with it).
Though, I do think you can be born with a greater tendency to be shy or submissive in nature. Or of course, the opposite, aggressive and dominant. But I don't think it's written in stone from birth. We've learned most of our behavior.
See it as a ball rolling down hill, the shape and size of the ball is not enough to go by to estimate its exact path. It can go either way. ;3