No, you will not be fined. In all likelihood, if the return you e-filed through the other service was accepted, the return you filed with TurboTax will be rejected. Wait until you learn whether or not your e-filed TurboTax return is rejected or accepted. If the return is rejected, you can go ahead and prepare to file the state return, but it will need to be paper filed by mail since TurboTax is not designed to e-file the state return on its own.
The following TurboTax return gives instructions for printing and filing your return by mail. https://ttlc.intuit.com/replies/3401713
