On Ellis Island (1890's) did detained children have to be with an adult?

No the child would have been removed form the ship in the outer harbor and transported to either Hoffman Island and Swinburne Island in Richmond County, New York. Their families would continue onto Ellis Island where they were probably detained while awaiting the sick child. Eventually, their families would have been released from detention on Ellis Island and traveled on to their new homes. If the child died while in quarantine the family would be released often never knowing where their children or family members were buried.