According to Kester's "Green Corrosion with Rosin Flux?"
The green is not an oxide. It is copper abietate. It is harmless but also green in colour like other harmful forms of copper corrosion.
It is formed when the abietic acid in the flux reacts with copper (particularly when heat-activated).
It is just the flux doing its job and reacting with the pre-existing oxides on the copper to remove them from the bulk copper surface to expose the clean copper below...except in this case it has nowhere to go and nothing to displace it (i.e solder). Copper that has no oxidation to begin with would not produce this green residue.
You can tell your customer this. It's nothing to be concerned about since it is not an actual corrosion product of copper.
Of course...unless it's due to chlorine released when PVC insulation is heated which might produce Coppper II Chloride (I'm not sure) which is also green but actually is an undesirable corrosive contaminant.
Either way, it doesn't seem like there is anything you can do about it other than not to dip the entire stripped end into flux. Even if you don't, it might wick up.