When are Roth conversion taxes due?

It was my understanding that if you completed a roth conversion let's say in November, the taxes are not due until you pay your federal and state taxes by April 15th of the following year. 

 

Even though I opted to pay the full amount of taxes for my November Roth conversion in December/January as a 4th quarter payment,  Turbo Tax included a penalty amount on my federal and state return. Please note that I am to receive a refund for both.  The 1099 R does not reveal the month of conversion; therefore, am I to assume this conversion is taxed for the entire year?  Please help.