Yes, you would expect that you would find yourself handing over the money. If told "Omega will soon predict that you will give him $5", then you divide the universe into two categories - I will give over $5, or I won't - and assign much greater probability to the first option.

But that is not a reason to give him $5 if you otherwise wouldn't. It's a reason to expect that there will compelling reasons to make you do it - but if these compelling reasons don't materialise, there is no reason for you to act as if they were there.