For the most part. I think that describes most of it. As for his mentality, he believes that things are the way they were always supposed to turn out, that messing with time is messing with the balance of the universe. How I see it, Jack is also possibly trying to keep the timeline the same so that he can continue his purpose, which is eventually killing Future Otori and succeeding him. As for his jealousy, it might also be because Jack was programmed to fight Takoizu. Otori apparantly wanted to see who was worthy of killing him and either taking over or killing the Neo-Yakuza, so he programmed Jack to fight her.
Spoiler:
It seems that Jack is also a way for Future Otori to hold on to Shikieiki after she died. He was not created just to succeed Otori, but also to somehow curb Otori's grief.
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