The linked research only describes phenomenological characteristics of illusions, so it doesn't strike me as an explanation. But it points to research that does

The linked research only describes phenomenological characteristics of illusions, so it doesn't strike me as an explanation. But it points to research that does attempt to explain the peculiarities of what conditions these illusions arise. For example, it seems to explain the effect of the brightness of the background on these motion illusions : First, an optimised stimulus can induce motion aftereffect on a stationary sinusoidal grating, which provides evidence for the activity of the visual motion mechanism. Second, perceived direction can be altered by background luminance. The local mean luminance seems crucial. On the basis of these findings, we propose that asymmetric responses of motion detectors to the jittering luminance gradient are the source of this illusion. A gradient model of motion detectors, which takes the image velocity as local temporal gradient over local spatial gradient, can predict such asymmetric responses if we assume imbalance in the positive and negative parts of temporal derivative filters. The asymmetry then depends on the DC offset of the stimulus, which explains the effect of the background luminance. From http://www.perceptionweb.com/abstract.cgi?id=v031085 http://www.perceptionweb.com/abstract.cgi?id=v031085