Omega only appears conditionally on at least the statement it asserts being correct. By taking/not taking its offer, you are only controlling the conditions under which Omega appears, and not contents of the envelope. By refusing the £10, you make sure that Omega appears only when the envelope is full (but you don't make the envelope full, though it's going to be full given that you've made this decision), and by accepting the £10, you make sure that Omega appears only when the envelope is empty.

It's admittedly confusing that you can (acausally) control the conditions under which Omega appears (when the envelope is full/empty), when Omega remains right in front of you during the decision-making (this is analogous to controlling the contents of the big box in Newcomb's problem) but at the same time, you don't control the contents of the envelope.