For your 2016 tax due?  You might be confusing the 4 quarterly ESTIMATE payments for next year 2017.  Were the 4 slips labeled 1040ES?  Those are for next year.  Did the IRS say you hadn't paid 2016 at all?

The way you handle it is to pay what the IRS says you have to pay. The late-payment penalty and the interest are charged because you did not pay the full amount of tax that you owed by April 18. Penalties and interest will continue to be added until you have paid the entire amount due. Having a payment plan lets you pay over time, but does not eliminate penalties and interest. It doesn't change the fact that you are paying late.

It's not TurboTax's payment plan. It's an IRS payment plan. You used TurboTax to submit the application for the payment plan to the IRS, just like you use TurboTax to send your tax return to the IRS.