Hopefully someone with a Korg Kronos will respond.
The information about the global audio settings on page 179 of the Operation Guide is rather sketchy, but it does mention that you must turn off (uncheck) the "Use Global Setting" parameter if you want to use a mic input with a vocoder, which I assume goes for any other "non-default" setup. So it might be that one thing to verify is whether that parameter is checked or unchecked.
Pages 8 and 9 mention that you can isolate audio inputs to the four "(INDIVIDUAL) 1...4" audio outputs, so it sounds like you should be able to do what you're wanting.
Page 21 also mentions that you can route various sources-- including audio inputs-- to the various audio outputs by setting the "Bus Select" parameters as desired. It also mentions that you should use one or another page of the "Bus Select" parameters depending on whether or not the signal is going through any insert effects, so make sure you're using the correct page of the "Bus Parameter" settings.
Note that page 21 refers the reader to page 771 of the Parameter Guide for more information.
Pages 22 and 23 mention using the "Audio Input" page to set the bus routing for the inputs, and refers the reader to page 19 of the Parameter Guide for more information.
I haven't tried to dig any further, but it sounds like you might want to check out page 19 of the Parameter Guide and go from there.
