You don't have to buy the cable kit exactly but you will need a custom cable or you will need to modify a cable because it is not a common cable. Ideally you will have a TRS to dual mono cable like we have in the QuNexus cable kit but if you want just a gate out with no pitch information you could also use a TRS to TS (also called mono) cable where:
1. The ring of the TRS side is wired to the tip of the TS side
2. The tip of the TRS side is discarded.
The reason why you were getting steps moved is likely because the pitch cv is being routed to your Volca's sync input. You may have hit a low enough note that it was under the Volca's gate input voltage threshold followed by a note high enough to trigger the sync input. You could test this by sending a series of notes that alternate between the lowest note and the highest note (C0 - C7). It may take several alternations to move one step or the sequencer may move once each alternation.
While the QuNexus is in your mobile rig, am I correct in assuming that you are going to want to use the QuNexus for a reason other than a clock generator? If so you may want to use out CV2 or CV3 for this task. You can program a pseudo gate by drawing in CC automation on a MIDI clip in Ableton Live. The automation will look like a square or pulse wave - full on then full off, alternating in a loop. If my theory about why your chords were advancing the sequencer then you should be able to use your existing cable with CV2. If my theory was wrong then you would need a new cable.
For more help with how to automate with CC data for QuNexus CV conversion you may be interested in a tutorial I made on the KMI Blog:
http://www.keithmcmillen.com/blog/seque ... onversion/
Let me know what you find!