First of all, look at the actual tax forms, not a summary screen in TurboTax.
Secondly, long-term and short-term gain are combined in one line on Form 1040 line 7. To see the separate amounts you have to look at Schedule D. Is your total short-term gain on Schedule D line 7 and your total long-term gain on Schedule D line 15? If so, the tax calculation will use the separate amounts. If they are not separated on Schedule D then you entered something incorrectly.
The long-term and short-term gain being combined on Form 1040 does not mean that they are being taxed at the same rates. The tax calculation uses the separate amounts from Schedule D. Since you have long-term capital gain the tax is probably calculated on the Qualified Dividends and Capital Gain Tax Worksheet, or possibly on the Schedule D Tax Worksheet. You have to look at the worksheet to see the calculation.
