LDS Pilot Site lists births for 3 children in Plumbrige district:
James born 4 Apr.1865 (mother Rosy Mcanenny)
Mary born 25 Apr.1867 (mother Rosy McAneny)
Michael born 12 Sept,1870 (mother Rosy McAnneny)
The family are shown in 1880 U.S. Census- Manhattan, N.Y.:
William Mullen, 46, Ireland, blacksmith
wife Rose Mullen, 46, Ireland, keeping house
daughter Mary Mullen, 13, Ireland, at school
daughter Margaret Mullen, 11, N.Y., at school
daughter Rose Mullen, 19, N.Y., at school
son William Mullen, 4, N.Y.
daughter Catharine Mullen, 2, N.Y.
Is this the family in 1901 census?
www.census.nationalarchives.ie/pages/1901/Tyrone/Plumbridge/Lisnacreaght/1752992If so, it gives William's birthplace as Co. Tyrone not Co.Londonderry.
Possibly son James married and with family in 9111-
www.census.nationalarchives.ie/pages/1911/Tyrone/Plumb_Bridge/Lisnacreaght/849403Mullin, Mullan, etc. is too common a surname in Northern Ireland to make assumptions about connections based on a common occupation such as blacksmithing.
Here the link for the Clooney family and all listed as being born in Co, Derry.
www.census.nationalarchives.ie/pages/1901/Londonderry/Benone/Clooney/1523409