In theory just white balancing a reference target wouldn't fix the issue. In practice the issue doesn't seem to present notable problems.
I always have to chuckle at color accurate claims - unless it's super refined work there are so so many factors that kill color workflow, that a swing from one setting to another is a comparatively small issue.
The color of the subject's shirt kicking back into their face; the age of the diffusion material in front of one strobe versus another; incidental reflection; mixed sources like ambient and strobe. From my experience, there are smart things to do, like throwing down black fabric at the subject's feet, isolating them from tungsten or fluoro, book end them with black or white… provided all your light is in the same general ballpark, you work to minimize any overt cast, things look really clean.
And for any problems some Luminosity Mask, to Apply Image, to a Curve for shadows vs highs will bring everything in to spec.
I guess I did mix them up here, in fact I had 3 different kinds of flashes. The TT685s, AD200s and an AD360...
I didn't see any issues in this 2 week shoot either, so I don't think it is really a big deal. I also shoot a custom WB, so maybe that takes care of things.