The forces push the rotating body of liquid outwards against the cup walls, at both the top and bottom, but because of friction effects with the cup’s base, the liquid at the bottom of the cup rotates more slowly, and is pushed outwards more weakly. So the liquid at the top of the cup “wins”. Liquid moves outward at the top of the cup, moves downward alongside the walls, and forces itself inward at the bottom of the teacup, while the liquid that was originally at the bottom gets forced inwards and upwards as a rising column of liquid at the centre of the cup. The tealeaves get caught up in this vortex flow and dragged to the centre of the cup, but the upward current isn’t strong enough to completely lift them, so they collect as a pile in the centre.
Einstein wrote a nice paper describing and explaining the effect.