I've had a quick look at this, and on the face of it I cannot see any obvious evidence of an Irish connection. Where did you come across that?
The death index listing of Euphemia Mary Yuill in 1976 says that her other surname was Davidson and her mother's maiden surname was Fowler. She was 81, which if accurate gives a birth year of 1894/1895.
There is no birth listing of Euphemia Mary Yuill in Aberdeen in 1894, or indeed anywhere else in Scotland at any time. There is a birth of Euphemia Mary Fowler, daughter of Samuel Davidson Fowler and Grace Turner Fowler, maiden surname Proudfoot, in Aberdeen in 1894. In the 1901 census this family is at Gracemount, Culter, Peterculter.
Samuel Davidson Fowler was born on 11 July 1861 in Culsalmond, Aberdeenshire, son of Alexander Fowler and Mary Sim, who were married in Culsalmond in 1843. I can't find a death. Both his parents were born in Aberdeenshire, Alexander in Inverurie and Mary in Culsalmond.
Grace Turner Proudfoot or Fowler died in Cookney in 1916, aged 54. She was born in Leith in 1864, daughter of David Crawford Proudfoot and Euphemia Rogie Stewart, who were married in Kinfauns, Perthshire in 1864. There was a death notice in the Aberdeen Weekly Journal: At Muchalls, Kincardineshire, on the 16th inst, Grace Turner Proudfoot, wife of Samuel D Fowler, and eldest daughter of the late David C Proudfoot, City Surveyor. Edinburgh, aged 54 years. Both of her parents were born in Perthshire, David in Perth and Euphemia in Longforgan.
As Euphemia's grandparents were all born in Scotland in the 1820s, any Irish connection is well before the start of statutory registration.