The codes on the Forms 1099-R are correct, you must not change them.
What TurboTax told you is that the distributions are not subject to "additional taxes," i.e., the 10% excise tax (penalty) on early distributions; code 2 means no penalty. Check your Form 8606 Part II to see how much of your Roth conversions are being treated as taxable. Also check Form 1040 line 4b.
