there is no 'feedback' loop from the IRS to Turbo Tax. The information sent to the IRS is confidential and not shared by the IRS with anyone but you.
so if you filed via Turbo Tax and Turbo Tax said you owed and you paid that money to the IRS, that is probably why the IRS website reflects zero.. did you check your transcript at IRS.gov?
TurboTax will always show the amount that you owed when you filed your tax return. It never gets updated after you file.
You didn't give any information about timing or what you have or have not done in terms of filing or paying. Another possibility is that the IRS web site shows a zero balance because they have not received your tax return yet, or have not processed it.
The amount shown in TurboTax that you owe the IRS will never change. It's just like when you receive a bill from your water company. When you pay the water bill, the amount shown on the bill you received does not magically change. It will always show the amount you owe to the IRS forever, weather you actually pay it or not.