I am an Indian citizen who moved to the United States on a J-1 visa. I worked for one employer for just over two years before moving to another employer for whom I worked for one year. I am now working somewhere else, on a different visa, and want to apply for permanent residence soon. While going through my old W-2 forms, I have noticed that my second employer did not withhold FICA taxes for the one year of my employment there.
AFAIK J-1 visa holders are exempted from FICA taxes for their first two years in the country. I thus believe that my second employer should have withheld FICA taxes for the entirety of my employment. I have spoken with the payroll manager at the second employer who agreed with my assessment but said that there is nothing they can do about it now. I have already filed taxes for the year in question.
My questions are (a) is there anything I can do to pay the FICA taxes that my employer should have withheld and (b) how likely will this come back to bite me in the future? I would be very grateful for any advice as I am a bit freaked out about not having paid the right amount of tax.