People make honest mistakes in filing their returns. And the IRS makes honest mistakes in entering data which makes it look like you owe more (or less) than you do.
I have received several notices from the IRS over the decades noting discrepancies between what I reported and what they received. They just politely asked for more money. Usually they were right, but in one notable case, they entered several items of data incorrectly and presented me with a notice saying I owed them several thousands of dollars more. (This was shortly after a government shutdown, when they had large backlogs and were overworked.) I examined their letter and my return and wrote them back refuting every point they made (politely, of course). They wrote me back, not exactly saying that I was right, but saying that, upon reviewing the correspondence, I owed them $0.00.
The IRS is not going to audit you for a discrepancy of $13.00, even if the discrepancy was in your favor, not theirs. If the discrepancy was in your favor, the IRS will send you a notice saying that you owe more money. In your case, I don't know if they will just send you a check for $13.00, but they might.