By default, individuals who enter with J visas as teachers/trainees are exempt from counting days for the substantial presence test for 2 calendar years: the year of entry and one more. This is regardless of the date of entry, so the number of exempt days can be anything from 366 to 761.
So a J visa holder who stays 183 days in a third calendar year will normally become a tax resident in that year. He starts counting days on January 1.
However, the writers of this law foresaw that some people might try to exploit the system ("exploit the system" here means "avoid paying US taxes", something the government strongly disapproves of ) by closely spaced visits on separate J visas. So here is what the code says, IRC 7701(b)(5)(E)(i):
(i) Limitation on teachers and trainees
An individual shall not be treated as an exempt individual by reason of clause (ii) of subparagraph (A) for the current year if, for any 2 calendar years during the preceding 6 calendar years, such person was an exempt person under clause (ii) or (iii) of subparagraph (A). In the case of an individual all of whose compensation is described in section 872(b)(3), the preceding sentence shall be applied by substituting “4 calendar years” for “2 calendar years”.
An example will help. Suppose X was first present in the USA as a student with an F visa in the years 2015 and 2016. She was exempt from counting days during those 2 years because she was a non-resident alien student, exempt under IRC 7701(b)(5)(A)(iii). Liking the experience, she returned in 2018 on a J visa for a 2-year teaching position. She starts counting days the day she arrives in 2018, just as though she were here on a work visa (for example H or L), because her 2 days of exemption under the J visa were used up in 2015 and 2016, which are within the preceding 6 years.
A further example: for tax year 2018, the past 6 years are 2012-2017. Let us suppose X had been here as a student in 2011-2012, not 2015-2016. Only one of her past years of exemption would fall in the past 6 years, so she would retain her exemption from counting days in 2018. Then, in 2019, the past 6 years will be 2013-2018, so she will be exempt in 2019 too.
The reference above to section 872(b)(3) refers to a situation where a non-resident student or teacher receives income from outside the US - usually a stipend from a government or university in his home country. Section 872(b)(3) exempts that income from US taxation. In that case different rules apply for determining exemption,as seen in the flowchart in Pub 4011, but the basic idea is the same.
I hope that is helpful. If you post a follow up please provide the details of your situation, in particular dates of visits to the US, visas you held, and your nation of citizenship.
