As the magnet falls, a mirror image field created by eddy currents, forms below the lower magnet, and into the tube wall. This field is the same polarity as the magnet and therefore opposes the fall. At the upper end of the magnet, a field opposing the fall is also formed. This field must be of opposite polarity to the upper magnet pole, as it needs to pull back on the magnet to oppose the fall.
As can be seen in Fig1, a field is shown outside the tube. Just as a magnet must have 2 poles, so also must a mirror image magnet have 2 poles. The eddy currents, while not shown here, would be in the tube wall. directly between the blue and red fields. This seems logical, as a long ring magnet mirror image is formed, with the NP on the ID, and a SP on the OD. This looks good, but does not occur.
Tests I have performed to determine the location and polarity of the fields generated by the falling magnet do not conform to this arrangement. The tests utilize Hall Effect sensors, 1 for North Pole and 1 for South Pole mounted about 10mm from the outer tube wall, with LED lights for visual confirmation. The actual fields are the real magnet's fields, and can be seen below.