Here are two articles from Prologue Magazine on the U.S. National Archives website that may be of interest regarding naturalization status of family members when the head of household is formally naturalized. It has a long and complicated history.
Women and naturalization, part 1:
Women and Naturalization, part 2
FINKELSTEIN, BOOKSTEIN/BUCHSTEEN, ALPER, LISS/LYSS, LEAF, LIFSCHITZ, LUSMAN