A tippe top is a little more than a hemisphere and a cylindrical stem. (The red axis here is shown for reference and is not part of the top.) The top starts its spinning on the rounded part. At a certain point it flips over to spin on its stem. This Demonstration models only the kinematics of the behavior.
An actual tippe top turns upside down in its motion due to a torque exerted by the force of friction at the contact point.