Omega (who experience has shown is always truthful)

Omega doesn't need to simulate the agent actually getting the reward. After the agent has made its choice, the simulation can just end.

If we are assuming that Omega is trustworthy, then Omega needs to be assumed to be trustworthy in the simulation too. If they didn't allow the simulated version of the agent to enjoy the fruits of their choice, then they would not be trustworthy.