Today I accidentally solved this problem.
Firstly I will remind the flow I can reproduce the bug - I open Classic Orchestra template and put a single note for oboe in second bar. Then I press J for JumpBar and start typing phrase “Dupli…” so I can select “Duplicate to Staff Above” with the mouse from the list. It copies selected note to staff above. It’s okay.
Then I press J again for JumpBar - it has the same command filled in a field and I press Enter. It copies already duplicated note back - down (I have double note for oboe) as if I was select “Duplicate to Staff Bellow”. Next time I open JumpBar it shows “Duplicate to Staff Bellow” which I never selected.
@pianoleo responded that he was unable to reproduce this bug and I start thinking it is because the way through updates and testing workflows are different for us.
Today while I testing Ctrl+Z (Undo) bug someone reported, I tried again to reproduce my “beloved bug” with JumpBar and as I wrote above I can replicate it. Then, I would say it happened accidentally, on a second step when the selected note is duplicated and on next try it would duplicate back, I just “walk” in JumpBar’s list (without expanding it) with keyboard key Down (it expands the list) then Up and Down to select “…Bellow” and then “…Above” again. Then I press Enter and it copies above.
Since then I cannot replicate this bug and we can assume that it is solved. How? Let’s ask developers/programmers - what was missed in JumpBar’s function that caused this bug and what was fixed after I walked through list with cursor keys? Some kind of ID stored temporarily or permanently and was lack of it until cursor key actions?
Now even I select Above or Bellow with mouse click, it works as expected.
So if someone has the same behavior, try to select options with cursor keys.
Thank you both, @pianoleo and @dspreadbury for your patience 
EDIT: removed “solution”, because nothing’s solved. (and I also have patience! …limited, of course)