I never done this on Cubase yet, but I did on FL Studio.
1. USB connection is not best for this, try if you can use MIDI connection.
When you play style on Korg, midi channel is mapping different that Standard.
Style using 9-16 channel. When you using MIDI OUT you can specify on which channel you put which track.
System Exclusive is using by Korg, but this data is a customize messages create by manufacturers and is sending by Korg, but is not readable by DAW.
System Exclusive not holding setting for effects, Program change and Control Change sending parameters for effects.
Try download free program MIDIOX from
http://www.midiox.com/
You going to see what data is sending.
The biggest problem is mapping channels, when you try read midi from Korg beside Style channels track you map others like Upper/Lower tracks, pads or even chord playing.
Template you got is only basic, design for basic style correction, you need customize it.
If you try make perfect template,....is possible but you never going to have exactly same as Korg, unless you going to use same Sounds generators.
Check in your manual section about MIDI Controllers, you see there available parameters which can go out and in.
Before you record on your DAW you need set tempo and Time Signature, I don't know if is possible to receive this from MIDI sending.
I never work with Cubase template yet, but if this is assign to MIDI Out Plugin, never going sound same, you may need later change plugin to similar you by KORG, many data record in DAW by default is not visible, but is all there.
If you record Guitar Tracks, all notes, data is complete different that others, velocity is using to assign Chord Shape not standard velocity of note.
Bottom line is is all possible, but if some point is pointless, believe me, I did try and now I like better dealing directly with instrument.
I do like sometime testing style using tracks recorded on DAW, but playing on Korg using MIDI IN, especially Guitar tracks, but recording I prefer audio record coming from KORG.
