I'm not sure how much you know about this, but the neodymium magnet falls through the tube slowly because the copper tube resists a change in flux. Flux is kind of like how much magnetic field something is being exposed to. Say the top of the tube was being exposed to the north end of the magnet. The tube wold then become a north at the top to resist the magnet getting closer to it and creating more flux. When the magnet starts to fall down the tube, the top part of the tube is used to the extra flux, so it tries to resist losing it by turning into a south pole (attracting the north pole). It's not really the ends of the tube that are causing the magnetic to move more slowly, it's the whole copper pipe in general. Seeing as the magnet does eventually fall through the tube, the force of gravity on it must be stronger than the force of attraction/repulsion created by the tube. Covering the bottom part of the tube would slow down the magnet even more because it creates more area to receive flux, and therefore to resist it. However, considering the weight of Nb, the magnet would probably hit the bottom.
