Yes, the IRS always make adjustments if there are errors, and they will send you a new statement/bill. I have never gotten a "refund" because of my errors, but it can happen. The IRS "fixes" my returns at least five times in the past... I usually end up owing more money.
They have their internal systems to cross check and recalculate your taxes based on the data in your tax returns as well as data they have (e.g. your W2s, your investments, etc.) the IRS knows! In this case, they would just change it based on your filed returns instead of asking you to file an amendment, since they know exactly what to change (by giving you the -$10,200 credit). You only need to file an amendment if there are things the IRS doesn't know.
