White balance controls are based on how real light sources are described in color science.

The temperature axis follows the color of an ideal blackbody radiator as it heats up: lower color temperatures look warmer (red/orange/yellow), and higher temperatures look cooler (white to blue). Many natural and practical light sources fall on or near this path, called the Planckian locus, so it is a useful way to describe white light.

The tint axis is the adjustment away from that locus. In camera/raw terms, this is usually a shift roughly perpendicular to the blackbody path, often described as green to magenta. That is useful because many non-blackbody light sources, such as some artificial lighting, are near a given color temperature but still have a green or magenta cast.

So the directions were not arbitrary: temperature comes from blackbody color in Kelvin, and tint is a correction off that path. Depending on the color model or diagram, the exact appearance of the axes can vary, but in photographic practice they are commonly presented as blue–yellow/orange for temperature and green–magenta for tint.