The mathematical model for a tippe top is a sphere with an uneven concentration of mass along the vertical axis, making the lower half heavier than the upper half; a physical model is more practical if you cut the top off the sphere and replace it with a stem. In each case, the key feature is that the centre of gravity is lower than the centre of the sphere. When the top spins, with the help of friction, it slowly tips over — raising the centre of gravity — until it is upside down.
If you want to really understand why it inverts, Richard Cohen was the first to provide a rigorous explanation in The Tippe Top Revisited Am. J. Phys. 45, 12 (1977). Or, if it’s important that you also know why it falls back down as it runs out of spin, see this paper.