Unmoving copper also neither repels or attracts a magnet.
Eddy currents impede movement of non ferrous metals in a static magnetic field. This looks like slow motion falling or resistance to spinning when the metal is in a fixed field.
This is how auto belays work.
If you move the magnet, the metal will also move since you're inducing a current and the fields from the eddy currents will react against the moving magnet.
That said, I'm enough of a layman not to be able to connect this explanation to what I saw in the video.
Are you saying because it wasn't moving in "slow motion," we can rule out non-ferrous metals? Or are you saying the alternating movement/stillness of the magnet shows this?
If you move the magnet, the metal will also move since you're inducing a current and the fields from the eddy currents will react against the moving magnet.