Dustin Kensrue tuned his Variax to D standard and had no problem.
I have always tuned my Variax transplants to D standard and never had any problems. My JTV on the other hand does not like to be tuned to D standard and makes funny out of tune notes on some of the models, the 12 string acoustics and the 12 string Rickenbacker are the ones I had problems with but there might be more.
A support ticket was created by another user here with the same problem and the results were:
"they've updated their faq's webpage to include that tuning must be in E Standard to work. They told me that that is how the guitar is calibrated and it's not tested beyond that. "
My JTV works properly when tuned down to Eb, and most models are okay when tuned down to D - but when tuned to D the 12 strings are mostly unusable, unless you are playing in a Japanese noise band or something.