If you have been present in the US for more than 183 days in 2019, you are considered as a US resident. You will start paying the FICA from January 1st, 2019 after you complete your five-year-F visa period.
As TurboTax does not handle your FICA exemption issue, I will suggest you communicate with your employer to resolve the issues. They might need to issue you a corrected 2019 W-2, that you may need to amend your tax return later. I am including a post from user Lisa Br who provided a very helpful answer to a similar question. Click here FICA withholding
Employers who do not comply with the employment tax laws may be subject to criminal and civil sanctions for willfully failing to pay employment taxes. For now, you will still file your 2019 tax return as usual. If things need to be changed on the W-2, you can always amend later. I am also attaching the following links for your references:
Employer vs Employee responsibilities
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