UPDATE: Emma claims to have lived in the United States before the Centennial, and to have come into the country in 1872 on a later census form. Still no evidence that this was the case.
Today I found proof that the Emma Allison who married A.D. Marchand in 1887 in California is the same Emma Allison who worked at the Centennial Exhibition. This proof opens up a lot more questions but also confirms the part of the story that Emma (and her mother and maybe some siblings) moved to California. Presumably this would be in 1877 after her father dies that year.