STEM OPT F-1 Visa FICA and Medicare taxes

I currently pass the substantial presence test and I have to be paying social security and medicare taxes but my employer is not in the same page. I wanted to know if I came to the US on 8/14/2014, do these taxes have to start to be withheld on 8/14/2019 or would it be starting on 1/1/2019?