Age does make a difference. On the income eligibility chart there are different guidelines for children and adults.
If a couple has a 18 or below year old child he is covered based on their income level. When he turns 19 I assume he would need to reapply as an adult (and I'm not sure whether he should use his parents income level if he lives at home and is fully supported?) and would have a higher barrier to entry to be covered.
Income Eligibility and Cost
NJ FamilyCare covers: children, pregnant women, parents/caretaker relatives, and single adults/childless couples.
Children 18 and under are eligible with higher incomes up to 355% FPL ($7,174/month for a family of four). Parents still need to renew the coverage each year.
Parents/Caretaker Relatives with income up to 138% FPL ($2,789/month for a family of four) must have tax dependent children in their household in order to be eligible under this category. Dependent children in the household must be insured also.
Adults without dependent children among ages 19-64 with incomes up to 138% FPL ($1,354/month for a single person and $1,832/month for a couple).
Pregnant Women up to 205% FPL ($4,143/month for a family of four).
Therefore, the answer to the question: At what age do children stop receiving coverage from Jersey Care? is when they turn 19, but they can possibly get new coverage as an adult although there's a much more restrictive income level.