Thats just the preset configurations... for prefered brands only (it'll make your Mackie's sliders automatically control Live's faders, etc)
You'll just have to assign your Korg's controllers to the various stuff in Live manually (or download some special control map for your microkontrol.. but dont bother w/ that)
Its easy to do... as long as your korg or the midi port its using is activated in the Input box in the MIDI tab in preferences, you should be able to do this:
Just hit he MIDI button at the top right of the screen, next to the CPU meter...
All the midi-controllable shit in the interface should turn purple
Select something highlighted purple, track one's fader for example, and then move whatever it is on your korg you want to use to control it
When youre done hit the MIDI button again