Turbo Tax only calculates an estimated penalty based on your filing the return and paying by 4/18/16 ... the IRS sends an adjusted penalty + interest letter based on when they actually receive the payment. This is not an error of the program, it is the way the IRS works.
Contact TurboTax support and speak directly with a TurboTax support agent concerning this situation if you still have questions.
See this TurboTax support FAQ for a contact link and hours of operation -https://ttlc.intuit.com/questions/1899263-what-is-the-turbotax-phone-number
IF TurboTax does the penalty/interest calculation for you, it can only be an approximate value to get you close.
The penalty and interest that the IRS assesses depends on exactly what date the IRS posts the payment you make, and TTX cannot know that at the time you prepare and submit your tax file. Thus, there is commonly an additional bill from the IRS. No particular fault anywhere, just a normal complication that no one can do much about.
How could it be a mistake? 1040 line 23 even says ESTIMATED tax penalty. And did you go though the form 2210 section to try to reduce or even eliminate it? You can try annualizing your income. You can even leave line 23 blank and let the IRS figure it for you.
The amount Turbo Tax calculates on your return 1040 line 23 is only an estimate. Turbo Tax can not figure it accurately because they don't know exactly when the IRS or state will get your return and tax due payment. It's very common and normal and expected for the IRS or state to bill you for more or send you a refund.