Thanks for the quick reply!
It's not the acoustic sound of the guitar. I cannot even hear that. It is really the sound of the magnetic pickups coming through the speakers at the same time as the modelling is on. The problem becomes more obvious when using alternate tunings.
This has been reported already by other clients, for instance, this current post (more recently) or
https://line6.com/support/topic/2382-variax-ghost-notes/
https://uk.line6.com/supportarchivenew/thread/66211/
https://line6.com/support/topic/9837-my-new-jtv-69-has-bad-modeling/
Googling by "variax ghost notes" or "variax magnetic bleed" will lead to more results. Unfortunately, no post has given any proper solution to the problem. Some users even told they have contacted Line6 and Line6 being aware of the issue.
I have tried the Variax Standard at my local music store and worked like a charm. But both JTV-69 I ordered online don't.
Like in other posts, I can provide sound samples recorded directly (no mics) if necessary.
Any help will be more than appreciated!