the players only find out if [Omega] was right or wrong after all decisions have been made
If you observe Omega being wrong, that’s not the same thing as Omega being wrong in reality, because you might be making observations in a counterfactual. Omega is only stipulated to be a good predictor in reality, not in the counterfactuals generated by Omega’s alternative decisions about what to predict. (It might be the right decision principle to expect Omega being correct in the counterfactuals generated by your decisions, even though it’s not required by the problem statement either.)
If you observe Omega being wrong, that’s not the same thing as Omega being wrong in reality, because you might be making observations in a counterfactual. Omega is only stipulated to be a good predictor in reality, not in the counterfactuals generated by Omega’s alternative decisions about what to predict. (It might be the right decision principle to expect Omega being correct in the counterfactuals generated by your decisions, even though it’s not required by the problem statement either.)