Census data from familysearch.org below, plus Philippe Louis immigration record.
Is "Alba/Alma' Roses' maiden or middle name.
It almost looks from the census dates, immigration years, births of children, that Phillippe and Lillian b. Canada might have had a different mother????
They remained in Canada for many years after Joseph immigrated abt 1897 and (Rose immigrated abt 1900).
So maybe your Rose married a widowed Joseph in CT and had the other listed children?
U S Census, 1940 Jewett City, Griswold Town, New London, CT https://familysearch.org/pal:/MM9.1.1/KWMQ-YBG
headRose PoirierF 58 CANmarried dauLillian Poirier F 26 CAN dau Theresa Poirier F 21 CT sonGeorge Poirier M 17 CT
U S Census, 1930 Stonington, New London, CT https://familysearch.org/pal:/MM9.1.1/XM5T-QH3
headJoseph Poirier M 47 CANimmigabt 1897 wifeRose PoirierF 47 CANimmig abt 1900 sonPhillip L Poirier M 19 CAN immig abt 1916 dauLillian I Poirier F 16 CANimmig abt 1916 dauAntoinette M Poirier F 12 CT dauThersea M Poirier F 11 CT sonArsene Poirier M 10 CT sonGeorge Poirier M 7 CT
US New England Naturalization Index Philip Louis Poirier, 1918 https://familysearch.org/pal:/MM9.1.1/VX5R-DC
name: Philip Louis Poirier Address:Merchants Ave, Taftsville, CT event: Naturalization event date: 6/4/ 1918 event place: New London Cty., Connecticut birthplace: Canada Certificate no.1031(P 660)