I disagree. This is the way I initially taught the game as well. But its hard to get into those 5 phases before you give players an understanding of the major goal of the game, and that is to produce great events by tile collection and achieving other bonuses. I think by opening with teaching them about what events are and then getting into the phases, the phases will make more sense.
No, I agree. I always give people an introductory overview of 'what it is you are striving toward'; what are the goals. Then I explain the 'how'. I just don't always think of the introduction as 'teaching' so much as 'describing'.