The problem is that the midi messages get both to the QC, the GR and the VST instrument itself.
Configure your axiom to send CCs that you don't expect to see on a VST or if you can, have it split to multiple midi inputs. Try CC 101-108 for QCs. Worked for me with the Axiom 25 we have in class.
I have a Roland A500Pro, which has the cool bonus that it appears as two different devices. I've set the keyboard and pitch/modulation as Device 1 and the rest (knobs, faders, transport buttons) to Device 2.
Device 2 is routed to Generic Remote (btw, if you use the GR, just map the QCs there instead of in the VST Quick Controls).
If you can't do that, map the buttons/knobs to a different midi channel (Ch16 for example), and filter them out on the midi / instrument channel input transformer.
And another P.S, Cubase has undocumented support for Soft Takeover / Catch mode if you fiddle with the GR some. Let me know if you want that and I could help.