No TurboTax will not contact the IRS and pay the penalty. You need to do that yourself. Then file an accuracy claim with TurboTax and if it determined to be TurboTax error, TurboTax will reimburse you for the penalty. You have 60 days to file your claim.
https://ttlc.intuit.com/turbotax-support/en-us/help-article/intuit-account-billing/submit-claim-turb...
