Maybe I misread your question. I read the question as "Why doesn't the software automatically make the 4th quarter state estimate as paid in that year." 

Are you making a statement that you have entered the 12/31/YY entry as shown in this image and the software still treats the payment as next year. 

Your three points marked as - do not totally make sense to me. I am old and sometimes I get confused. I thought you were saying with your last statement "The software still allocate only the first three quarters payment in itemized deduction as if the last payment were paid in January 15 next year." that the software should read your mind - Last year I made the payment on 12/31 - Why don't you mark this next year the same way - You should know what I am thinking.