Duncan Davidson (who I still think of as James) asked on Twitter:

Color Temp works on the Blue/Yellow axis. Tint on the Green/Magenta. No need to tweak Red/Cyan?

I responded there but decided to here as well as I've talked about colour theory before.

The basic answer is that you only need two axes because colour (disregarding brightness/luminance) is two-dimensional. Red, Green and Blue form a triangle in that two-dimensional space (with Cyan, Magenta and Yellow being on the opposite edges respectively).

Basic linear algebra tells us that, in an n-dimensional space, you only need n vectors to form a basis (actually, that's the definition of dimensionality) so you can adjust any point in two-dimensional colour space by translating it by a linear combination of any two, non-parallel vectors. Incidentally, Hue and Saturation would be almost polar coordinates on this space.

Because one form of colour modification is colour temperature, it makes sense to roughly make one of the axes the yellow-blue direction. I think the magenta-green axes is largely arbitrary. Any other axis would have done fine.

Note I say "roughly" the first time in that previous paragraph because the black-body colours aren't a straight line in standard colour models.

Hmm, that makes me wonder if colour correction sliders represent rectilinear bases at all.

UPDATE (2008-05-04): According to a reply in the Reddit thread, the slides aren't rectilinear but are based on the black-body colours. The so-called "tint" is presumably then orthogonal to black-body line (the Planckian locus)