This Omega can easily prove that the world in which it asks you to pay is logically inconsistent, and then it concludes that in that world you do agree to pay (because a falsity implies every statement, and this one happened to come first lexicographically or something).
This seems to be confusing "counterfactual::if" with "logical::if". Noting that a world is impossible because the agents will not make the decisions that lead to that world does not mean that you can just make stuff up about that world since "anything is true about a world that doesn't exist".
Noting that a world is impossible because the agents will not make the decisions that lead to that world does not mean that you can just make stuff up about that world since "anything is true about a world that doesn't exist".
If event S is empty, then for any Q you make up, it's true that [for all s in S, Q]. This statement also holds if S was defined to be empty if [Not Q], or if Q follows from S being non-empty.
This problem is roughly isomorphic to the branch of Transparent Newcomb (version 1, version 2) where box B is empty, but it's simpler.
Here's a diagram: