A Turbo Tax professional submitted my taxes incorrectly after I paid for the service. I now owe back money, please advise.

You do not provide any details as to what you think the TT expert did that was incorrect.   

TurboTax guarantees the calculations done by its software.   The information entered into that software is data entered by you, the user or provided by you to your "Live" expert.   TurboTax cannot and does not check that information against any outside sources, so TT cannot know if you entered your information completely or correctly.   It is up to you to enter all of your information correctly and completely, and to check your tax return before you file it.  If you forget to enter some income, or enter it incorrectly, enter it in the wrong place, etc. then you may end up owing additional tax to the IRS and/or state.  TurboTax does not pay the additional tax you owe.   If TurboTax’s calculations were incorrect, and you owe penalties and/or interest, then TT will pay the penalties and interest.  The tax due is always owed by you, and must be paid by you.

If you need to enter a claim for the accuracy guarantee:

https://ttlc.intuit.com/turbotax-support/en-us/help-article/intuit-account-billing/submit-claim-turb...