You're okay. When you make contributions to a Traditional IRA (a "rollover" IRA), you're allowed to take a tax deduction for that contribution, if eligible. That's something you would enter into TurboTax each year and the software will make the eligibility determination based on your income and the questions you answer. If you're getting a deduction for the contributions, then you wouldn't be taxed twice.
But even if you don't get a deduction for the contributions, you still won't be taxed twice. That's because "non-deductible" contributions are considered to be your "basis" in the IRA, meaning the amount that's already been taxed by the time you contributed it. When you retire and start taking money out of the account, the non-deductible contributions are considered to have come out first, and they won't be taxed. Whenever you enter the amount taken out of an account, TurboTax always asks you if you made non-deductible contributions.
So you either make a deductible contribution and get a tax break up front, or you make a non-deductible contribution and get a tax break at the end.
You'll enter your Traditional IRA contributions by following this pathway: Federal Taxes > Deductions & Credits > Retirement & Investments > Traditional & Roth IRA Contributions.
