Why did what I owed on my state taxes get taken out of both my federal tax return as well as my personal bank account?

Have you received your federal refund?  A state tax due can NEVER be deducted from the federal refund.  At the end Turbo Tax just shows you the net combined amount for federal and state.  But that's only for you own info.  You will still get the full refund and  have to pay the state tax due separately.  You can only have the Turbo Tax fees deducted from a federal refund.  See,
https://ttlc.intuit.com/community/state-taxes/help/can-i-pay-my-state-taxes-from-my-federal-refund/00/26288

Check the printout or PDF of your return; look for the state cover sheet with the Turbotax logo. If you owed tax, it will show the payment information and how/when you decided to pay. Read the state payment instructions carefully since most states cannot be paid from within the TT system and requires additional steps.
https://ttlc.intuit.com/community/refunds/help/what-are-my-options-for-getting-my-state-refund-or-for-paying-any-state-taxes-i-owe/00/25954