J1, returned home and F1

F-1 visa Tax Exemption deals with the Social Security/ Medicare Tax Liability, which means that foreign students in F-1 nonimmigrant status who have been in the United States less than 5 calendar years are still NONRESIDENT ALIENS and are still exempt from social security/ Medicare taxes. Based on IRS Pub 519, F1, J1 students are exempt for up to five years during their status as a full-time student in the United States.

Non-resident alien students, trainees, researchers, physicians and other aliens on F-1, J-1, M-1 non-immigrant status temporarily present in the United States are exempt on wages paid to them for services performed within the United States as long as such services are permitted by USCIS and are performed to carry out the purposes for which for non-immigrant status visas were issued to them.

Exempt Employment includes:

On-campus student employment up to 20 hours a week (40 hrs during summer vacations).
Off-campus student employment allowed by USCIS.
Practical Training student employment on or off campus.
Employment as professor, teacher or researcher.
Employment as a physician, au pair, or summer camp worker.
Limitations on the F1 visa tax exemption:

The exemption does not apply to:

Spouses and children in F-2, J-2, M-2, or Q-3 non-immigrant status.
Employment not allowed by USCIS or to employment not closely connected to the purpose for which the visa was issued.
F, J, M, or Q non-immigrants who change to an immigration status which is not exempt or to a special protected status.
F-1, J-1, M-1, or Q-1/Q-2 non-immigrants who become resident aliens.
The Social Security/Medicare Tax Liability
The Internal Revenue Code (IRC) sets the liability for social security and Medicare taxes on both the employer and the employee, he who earns income from wages in the United States. The IRC also gifts an exemption from security/Medicare taxes to alien students, scholars, teachers, researchers, trainees, physicians, au pairs, and other nonimmigrants temporarily present or entered in the United States on F-1, J-1, M-1, Q status as a non-resident alien.