I suggest that what is happening here is that Omega establishes a causal link with the agent's decision to 1- or 2-box. Consider an analogy: You happen upon a group of crystals, each of which is anchored to the ground and grows upward with a complicated internal structure. Each is generally cylindrical to a minimum length, whereafter it continues in a helical fashion. Some crystals have a right-handed helix and others are left-handed. You, for reasons of your own, determine which are left-handed and at a point just below the start of the helix mark them, perhaps with a drop of ink. Omega has done nothing more than this. His mark is the contents of the opaque box. What the agent "should" do is to 1-box... that is, to turn left at the start of its helix... because that is the "moment" at which causality kicks in. No doublethink required.