@krissh1368 ,
FICA contribution is 15.3% -- generally shared 50-50 by the employer and the employee. The fact that your employer considered you a "student" means that they did not contribute their own share either. So to keep the system happy ( that is for purposes of your retirement ) you can pay in the 15.3% or you can convince your employer to pay his/her share ( a very unlikely event ). It may be easier to just let the sleeping dog sleep.
USCIS / DHS does not determine tax rules and regulations --- therefore I sent you quote from the IRS lawyers and as long as you met the conditions called out you should be immune from FICA. It is possible that all sides made a mistake but trying to correct it may become itself an issue , not the least of which is that your employer would look real bad ( even may be fined ) -- therefore I would suggest leaving it alone. IRS generally will not question this unless we are talking about Thousands of dollars in fines and taxes ( it cost them quite a bit to collect taxes/penalties) and if by some chance your 2018/2019 gets selected for a full audit ( an unlikely event but definitely possible ), you could then explain the mistake and let them take action/settle -- that way you will not make your employer unhappy ( especially since he is changing and collecting/contributing FICA here onwards.
Namaste
pk
