If Omega makes its prediction based on the past instead of the future, CDT two-boxes and gets $1,000. However, that is a result not of the decision CDT is making, but of the decisions it has made in the past. If Omega plays this game with e.g. TDT, and you substitute TDT with CDT without Omega noticing, CDT two-boxes and takes $1,001,000. Vice versa, if you substitute CDT with TDT, it gets nothing.
If Omega makes its prediction based on the future, CDT assigns a probability of 0 to being in that situation, which is correct, since this is purely theoretical.
If Omega makes its prediction based on the past instead of the future, CDT two-boxes and gets $1,000. However, that is a result not of the decision CDT is making, but of the decisions it has made in the past. If Omega plays this game with e.g. TDT, and you substitute TDT with CDT without Omega noticing, CDT two-boxes and takes $1,001,000. Vice versa, if you substitute CDT with TDT, it gets nothing.
If Omega makes its prediction based on the future, CDT assigns a probability of 0 to being in that situation, which is correct, since this is purely theoretical.