I remember I have seen this happening before. But I am not sure why this will happen and have not taken any video. Any explanation are welcome.
From my understanding, this can happens due to a difference in (gradient of) surface tension. This tension pushes the particles from the region of lesser tension to higher. [The fluid moves away from the region of lower surface tension, like a detergent in water.] This force on the surface of the water during the pouring can make the particles in the cup flow upwards. The effect should be stronger for lighter particles and a greater gradient of surface tension. This looks similar to capillary flows in trees, or tears of wine. See Maragoni effect and this video on tears of wine.
However, for a complete answer, I would need to explain why there is a surface tension difference. It normally happens when you have two different fluids, but in this case, both are water. Perhaps it is due to the difference in density when you add the leaves, but I imagine that it is needed a high concentration of tea dust on the surface of the water in order to give a reasonable surface tension difference (but I do not have numbers on this).