TurboTax does not pay your taxes. You input your payment account information into your tax return, TurboTax sends that to the IRS. The IRS debits the account that you provided, but there is no feedback from the IRS to TurboTax about that.
The proof will be in your statement from the account that you provided. You can also order a transcript of your return from the IRS which will show the amount that was paid.
You can get a free transcript of your return from the IRS:
You can get a complete copy from the IRS, but it costs money, see this link for how to get it: