Well the thing with these movies is that I think most of the adjustments might be done with curves, not hue/saturation/luminance. (They did this in FOTR though, since grey and blue was made cyan and then the luminance was dialed down a lot) Anyway, I'm not an expert but here's an example of using curves.

I take this Christmas fireplace photo from wikipedia:

First I reduce red and increase blue in the shadows up to the midtones. Then I increase green in all the picture, as well as reduce red and blue in the whites, just like they did with those films. Then some vibrance/saturation to make the colors "pop" a bit more.

Tadaa! Modern Hollywood film color timing.

EDIT:

I'll add something about Hobbiton too.

Take this natural photo of the shooting location:

In The Hobbit AUJ, when color timing the scenes in Hobbiton it looks like they changed the curves a bit to make highlights less bright and also added some green tint, resulting in something like this:

When you have nothing to compare to, and watch the movie like that you might not even notice the green tint.

In FOTR they used HSL to make cyan/blue dark and boost the rest and the result was a bit like this:

Bottom line: There's many aspects to color timing and of course changing fire to orange doesn't automatically change skies to cyan, but they just like doing it that way these days.