When I stepped through my test, doing business expenses first then the itemized deductions, I got the same result on desktop that I did online - I entered $20,000 as property tax paid with a 10% home office allocation (so I got a $2,000 deduction). When I returned to the itemized deductions on the federal return and got to Property Taxes, on the screen entitled "Enter the Property Taxes you paid", on the first line for 2017, my $20,000 total was already entered so I just hit Continue. Sure enough, on the next screen, TurboTax told me that "Good News: You qualify for a property tax deduction of $18,000. $2,000 is reported separately under your home office" which is correct.
So far, it looks like online and desktop look to be operating the same way, although I understand your point about possible confusion on what to enter. Even when I deleted TurboTax's $20,000 entry and coded $20,000 again (like you did), the calculations remained correct.
It seems you are on the ball and have done your own due diligence to verify that the deductions are correct and in the correct places. Since we on AnswerXchange can't see your screen, if you want to pursue this, I would suggest that you contact phone support where an agent (with your permission) can see your screen.
