Who reports to the credit agencies that a judgment has been paid in full?

The creditor or the court? I paid a judgment in full and the creditor said they still have a balance but later figured out that I actually paid. He said he would send a satisfication of paid in full or something. I paid in 2012 so I told him that he should put the correct date because I don't want it to say I paid today if I paid two years ago! He said the date doesn't matter and that the court needs to report it the credit agencies? What should I do.