I know no FTIs of any cut depth have been mass-produced yet, but they exist in virtual form so I'm hoping someone who is familiar with them can answer this.

Do FTIs have orbits like many other jumbling puzzles, and if so, does jumbling allow pieces to leave their orbits? If not, does that mean the FTI can always be solved without using jumbling moves even if it has been scrambled with them?

The pieces of all "normal" FTIs and VTDs don't have orbits with the exception of chiral pieces which have a right orbit and a left orbit.

You don't have to worry about chiral pieces appearing until you get to a depth of Gelatinbrains 1.2.4 for VTDs and 2.1.4 for FTIs.

Also, chiral pieces are a unique type of orbit problem. You can "invert" a chiral pair (they are in each other's spots) but this seems to require flipping around the pieces between them too. The puzzle is in an obviously jumbled state when this happens and once you unjumble it you don't have any problems.

So in short, you don't have to worry about any orbit issues for solving FTIs or VTDs.

Unjumbling VTDs seems to be non-trivial. I'm currently stuck trying to unjumble Luke's NovaMinx.

Thank you for the information! It's relieving to know that when Eitan's Star is released I won't have to learn anything extra to solve jumbling scrambles (well, other than unjumbling).