He was NOT getting SSI based on a deceased father and neither are the other children. SSI stands for Supplemental Security Income and it is not funded by FICA/OASDI payroll taxes, it is a needs-based program for disabled low income adults and disabled low income children and elderly low income adults (over age 65).
What the children get is Social Security Survivor benefits. I know that the words and acronyms are very similar and easily confused. Survivor benefits are not needs based. Children with massive trust funds and wealthy surviving parents can get Social Security Survivor benefits if the deaceased parent paid into the Social Security system for enough years by paying FICA/OASDI taxes.
Children's survivor benefits end when the child reaches age 18 UNLESS the child is still in high school on his 18th birthday. Then, the benefits continue until he is out of high school or turns 19, whichever is first. Decades ago there were survivor benefits for college students. Not now.

