I must admit I don't experience the convoluted opening you describe. I do get a huge whiff of eucalyptus, which, interestingly enough, is not listed on Zino's pyramid. (Maybe I'm smelling the clary sage?) After the somewhat "herbal medicine" opening, it dries down to a very strange and sexy fragrance of predominately sweet woods.
Zino Davidoff is often compared to Heritage Guerlain, but I find them only vaguely similar in the opening notes. I actually prefer Zino because I find it more sensual, bohemian, less "stuffy", and more individualistic than Heritage. Then again, I tend to like the fragrances that are a bit off-beat: i.e. Salvador Dali pour homme, Habit Rouge, Xeryus Rouge, to name a few. (I was disappointed that Luca Turin thinks Xeryus Rouge's composition smells "cheap." I disagree.)
PS: Heritage Guerlain's longevity is far superior to Zino Davidoff's. Heritage = about 24 hours. Zino = 6 hours for me, at best.