Presumably, if you use E to decide in Newcomb's soda, the decisions of agents not using E are screened off, so you should only calculate the relevant probabilities using data from agents using E. If we assume E does in fact recommend to eat the chocolate ice cream, 50% of E agents will drink chocolate soda, 50% will drink the vanilla soda (assuming reasonable experimental design), and 100% will eat the chocolate ice cream. Therefore, given that you use E, there is no correlation between your decision and receiving the $1,000,000, so you might as well eat the vanilla and get the $1000. Therefore E does not actually recommend eating the chocolate ice cream.

Note that this reasoning does not generalize to Newcomb's problem. If E agents take one box, Omega will predict that they will all take one box, so they all get the payoff and the correlation survives.