The purpose of Form 8606 (Part III) is to compute the amount of UNQUALIFIED distributions from Roth IRAs that is taxable. If your 1099-R shows code J or T, TurboTax will assume that the entire distribution shown in Box 1 is an unqualified distribution. In general, the Payer of the distribution doesn't know whether the distribution is qualified or unqualified because the Payer doesn't know what other Roth IRA accounts you might have elsewhere and when you made contributions or conversions to those accounts. The burden of determining whether the distribution shown on your 1099-R is qualified or not qualified is entirely on you the taxpayer.
Also, keep in mind that every time to take a distribution from your Roth IRAs, you must subtract the amounts that were distributed from your Basis in Contributions and Basis in Conversions.
