Stirring the cup of tea rotates the liquid and the leaves around the cup. However to rotate in a fixed path, the centripetal force must balance the centrifugal forces on leaves.
With no centripetal force, the centrifuge pushes the leaves far from the axis of rotation, towards the wall/rim of cup and creates a pressure gradient with high pressure liquid on the outside and a low pressure liquid on inside.
Thus, at the top of tea cup, the centrifuge is balanced by the force emerging from pressure gradient.
However at the bottom, the liquid experiences large frictional forces, which lowers the velocity of the rotating liquid. This reduces the centrifuge on the liquid and creates a low pressure region at bottom.
Therefore the force resulting from pressure gradient between the upper and bottom layer strengthens over the centrifugal force on the liquid. This makes the leaves to flow from the top to the bottom and collect at the bottom.