Whilst the magnet is falling through the aluminium tube the tube is in an area of changing magnetic flux, this induces small emf's in the tube and, as the aluminium is a conductor, these will drive eddy currents within the part of the tube that is in the area of changing magnetic flux. These currents give rise to electromagnetic forces that, by Lenz's law, oppose the motion of the falling magnet. In summary, whilst the aluminium tube is not itself a magnet, the relative movement of the falling magnet indirectly induces small magnetic fields in the tube, and these work to repel the magnet in the opposite direction to its motion, hence causing a braking effect.

I hope that's a good enough explanation!

emf = electromotive force

Yes it does,

But the aluminium tube is not magnetic...

Something is happening when the 'magnetic' blue object is falling!

But do you know what it is?

Does it have something to do with the heavy one being magnetic?