There are areas of this question that have yet to be answered. For example, a Thomas Dick was married to one of my distant cousins, Mary MacCallum. They had a child in 1873, so this is unlikely to have been the same Thomas who married Minnie. Possibly a father?
When Thomas Dick married Minnie, he was given as a widower. Sometimes he was called Alfred. For example the birth record with his first wife at: http://archives.gnb.ca/APPS/GovRecs/VISSE/141A2_2.aspx?culture=en-CA&guid=B2FB3975-6B34-4AEB-9F37-32A46DB8B087http://archives.gnb.ca/APPS/GovRecs/VISSE/141A2_2.aspx?culture=en-CA&guid=B2FB3975-6B34-4AEB-9F37-32A46DB8B087 gives a son as Thomas Edward Dick (born 16NOV1897) and names his wife as Catherine Currie. At: http://archives.gnb.ca/APPS/GovRecs/VISSE/141B7.aspx?culture=en-CA&guid=34F296CF-7507-41F2-8D40-4DF4F89E9C65http://archives.gnb.ca/APPS/GovRecs/VISSE/141B7.aspx?culture=en-CA&guid=34F296CF-7507-41F2-8D40-4DF4F89E9C65 Thomas Alfred Dick b. Glenelg Parish, Northumberland Co., NB ca. (about) 1871 married 19SEP1892 Kate Currie. He was the son of (s/o) William and Mary (Johnson) Dick. When he married Minnie: http://archives.gnb.ca/APPS/GovRecs/VISSE/141B7.aspx?culture=en-CA&guid=81C5D42C-6B31-4BB1-91F0-3217D4D049D8http://archives.gnb.ca/APPS/GovRecs/VISSE/141B7.aspx?culture=en-CA&guid=81C5D42C-6B31-4BB1-91F0-3217D4D049D8 he is given as b. Chatham, the widower of the 'late Katherine Currie', b. ca. 1871 and the s/o William and Mary (Johnstone) Dick. Glenelg Parish is just across the Miramichi River from Tabusintac, which is where I would expect to find the Johnstone's (also cousins) so I think he was more likely born there than in Chatham. Also, Johnstone is more likely the correct spelling of his mother's maiden name. Making that kind of judgement in the face of conflicting data is a matter of experience. For example, Thomas Alfred Dick's son by his first marriage, mentioned above as Thomas Edward Dick, d. (died) in Gloucester Co., NB 30JAN1919 as Thomas Edmund Dick. If you were not familiar with the variableness of names and spellings you might think they were different people.
That Thomas Alfred was sometimes called Alfred (middle names were often used when one had a father and/or a son with the same forename), produced a couple more birth records for children with his first wife. He was, however, Thomas A. Dick b. ca. 1873 in the 1881 census of Chatham Parish. He was the s/o William (ca. 1826) and Mary (ca. 1831) Dick. Mary was b. in Ireland, so my theory that she was one of the Tabusintac Johnstone's falls apart at this point. William (b. ca. 1829 in the 1851 census) did come from Glenelg Parish. Unfortunately the NB 1851 census just became unavailable as it often does, so I cannot follow this up at this time.
Catherine Currie is very likely Katie Currie born about 1875, daughter of Thomas and Alice Currie, in Chatham Parish in the 1891 census.She was Thomas Alfred Dick's first wife. Kate (Katherine) Dick, wife of Alfred Dick, d. Chatham Parish 12DEC1916 (8DEC1916 in a separate death record, complications in childbirth) age 41 years (b. ca. 1875), and since she was born in Chatham Parish, certainly seems to be the same in the 1891 census. the 12 December date was likely when she was buried.