If by "nominal tax rate" you mean what TurboTax calls "effective tax rate," that's a useless number for understanding how an increment in income increases your tax liability. Marginal tax rate is what matters, the ratio of your change in tax liability to the change in taxable income, which you say is 25%. An increase in tax liability of around $1,100 (25%) for a $7,000 increase in income can easily result in a change from 15.1% to 15.9% in effective tax rate. It's certainly not being caused by a 25% penalty on anything.
As VolvoGirl said, to understand the reason for your change in tax liability you must compare your Form 1040 with and without this $7,000 of income side-by-side.
A change in effective tax rate of as large as it is when going from 15.1% to 15.9%, I would expect that your marginal tax rate would have to be close to 25%, particularly when you have tax credits such as the child tax credit.
