Turbotax calculates your cap gains tax on the Qualified Dividend/Long Term Capital gains worksheet, and that calculation is accurate.
However, if your income is high enough that you are subject to the Alternative Minimum Tax, you can be seeing a secondary effect. When you are subject to the AMT, you have a deduction which can be reduced. That deduction is reduced based on the amount of capital gains that you have. What that does is it still taxes the cap gains at your maximum cap gains rate, but the reduction in the AMT deduction means that more of your other income is subject to the AMT and your tax goes up by more than what you would expect from the cap gains tax alone. It is a clever way that congress found to increase cap gains tax without increasing the cap gains rate.
You can find the details of the calculation by looking at Form 6251 in your tax return. Or see a blank 6251 at this link:
https://www.irs.gov/pub/irs-pdf/f6251.pdf
