display calibration – When and how should I use the “hue” setting in the monitor?

If you are already individually adjusting the red, green, and blue brightness levels, then you should leave the hue adjustment set wherever it was when you did the RGB levels. I’d recommend leaving it at the “neutral” centered position before doing the RGB levels.

“Hue” in this context is just a quick and dirty adjustment along the magenta ←→ green axis that is more or less orthogonal to the amber ←→ blue color temperature axis.

When and why am I supposed to use it?

No one says you are “supposed” to ever use it. You may find it useful if you are viewing a source of images or video content that is biased along the magenta ←→ green axis. You can use it as a quick way to compensate while viewing that content.

How am I supposed to tune it?

If you are doing individual red, green, and blue brightness/saturation adjustments, then there’s no need to tune it. Any changes you make to the hue adjustment will require redoing the RGB adjustments to offset the change you made to the hue setting.

Just leave it alone.