Great Question!
Companies run EFTs (electronic funds transfers) all the time. You may already pay some of your bills this way. They would not stay in business if they made a habit of taking one cent more than authorized. Rest assured that Turbo Tax is a reputable company.
I do recall TT had a price increase in March, so the price may be more than you anticipate. Nevertheless, it will state clearly what amount you agree to, before you have to actually pay.
Of course it is a good idea to keep a close watch on the transactions in all your accounts, every month.
Best wishes.