Interesting illusion indeed.

Do it yourself: http://i.imgur.com/Bf8xi.jpg[/link

The whole cylinder/ shadow is just a distraction, so ignore that.
It’s evenly litted, the shadow has nothing to do with it.
The squares are 'painted' darker in the middle.

The darker squares and the light squares from outside are both darker in the middle.
Making the inside light square 'equally dark' as the outside dark square.

Making them equal tint wise. To 'switch'.