I would guess at a basic level they just tweak the Sodium dosage ratio to get the colour temperature to the point they want?
for example my 1650W Venture M112 metal halide lamp which is quite highly dosed in sodium due to its high power loading and special nature is a 3200K lamp
https://www.lighting-gallery.net/gallery/displayimage.php?pos=-237831https://www.lighting-gallery.net/gallery/displayimage.php?pos=-237874