Hi

Yes.  ALL my previous and current Variaxes initially had this problem inc my JTV-59 and JTV-89.

The 12 string models have to use pitch shifting obviously to achieve the second 'virtual' string in each pair of strings.

The 'virtual' string will have been preset to an octave up for four strings in each pairing and to the same pitch for the other two virtual strings (E and B).   Line 6's engineers have introduced a mechanisim for detuning each virtual string by an adjustable amount of cents and with an adjustable mix (volume) level.

The defaults are what you are using I guess as your guitar is so new.  In my humble opinion the default detune and string mix levels for all the 12 string guitar models have been way overcooked - but I have also noticed that the problem you are hearing can be perceived as somewhat better or worse dependent on what you are monitoring through.

Another thing which can affect the amount of 'warble' you hear is how good the intonation and tuning is on the guitar.  Both are important.  You might need to have the guitar set up as the factory set up with the JTV series, like any other new guitar is a standard but not necessarily perfect job.

There is possibly a slight underlying tendency for some warble given the nature of the pitch shifting process used anyway.

Here's what I've done with ALL my 5 VDI capable Variaxes to improve the situation so that it is not noticeable.

1. Update the Variax firmware to the latest version.
2. Load Variax WorkBench and adjust the detune for each virtual string to +/- 1 or 2 cents maximum
3. Adjust the mix level for each virtual string to 20% or 30%
4. Save the modified settings to the guitar
5. Adjust intonation and string action as necessary to be accurate and to avoid any fret buzzes
6. Take care not to mis-fret or be at all heavy handed in playing the guitar as heavy handedness can cause intonation problems as strings slightly bent too far by pressing too hard can drift plus, the JTV fret height is slightly greater I think than say a standard Les Paul or Strat - or at least it seems so

The main trick here is to make any warbling less noticeable, but I have to say it works for me and I am someone who prefers an accurately tuned 12 string guitar even with my real ones rather than an overly detuned and too 'jangly' one.

The current firmware version for the JTV series guitars is version 1.71 however in the last few days we have been given advance notice of a new firmware version coming soon which will feature 5 remodelled versions of the acoustic models in the JTV guitars including the two 12 string acoustics.  Hopefully this new firmware will address the problem you describe with respect to at least the acoustic 12 string models and hopefully the two electric 12 string models too.  The new firmware version is numbered 1.18 and other features have also been added which enhance working with a POD HD500 or POD HD Pro in other ways.

HTH

Regards

Nick