I'm afraid things aren't as clear-cut as you think.
Working back from the facts re. her parents on her 1881 marriage certificate. Her mother Margaret (Maggie) Finlay married James Buchanan 12/2/1864 Partick, Glasgow - both are shown as single!
I should add here that it was quite commonplace in Scotland for children born illegitimately and registered under their mothers surname to grow up with the surname of their father even though the parents never married. As you will also find particularly in Scottish records, female names have many variants as with Janet (Jessie, Jane, Jean etc.). (Just to complicate things further).
Angus McAllister and Margaret Finlay/Findlay never married and, as shown on the marriage to James Buchanan, she was single. Also, 'Jessie' certainly wasn't born 27/7/1858!
The 1871 census states she was 15, 1861 was 5, so a birthdate ca.1855/1856. Also, she stated she was 24 when she married (actually 25) in 1881 and none of these agree with the birthdate in 1858.
She was actually born as Janet Finlay on 29/12/1855 High Church, Glasgow, dau. of Margaret Finlay.
1861 Census - Lindsays Land, Maryhill, Glasgow.
Margaret Finlay 26 Cotton Yarn Winder b. Slamannan, Stirlingshire
Janet McAllister 5 b. Glasgow
James McAllister 2 b. Glasgow
James Buchanan 25 Lab. Agl. b. Kilbarchan, Renfrewshire
As you can see from 1861 census Margaret was already living with James Buchanan - dau. Janet is now McAllister as is a James - however, James would actually appear to be the son of James Buchanan as the next census shows - Janet McAllister is shown as stepdaughter!
1871 Census - 20 Ann St., Glasgow Barony, Lanarkshire
James Buchanan 35 Carter & Milk Dealer b. Kilbarchan, Renfrewshire
Margaret Buchanan 36 b. Slamannan, Stirlingshire
James Buchanan son 12 b. Glasgow
William Buchanan 7 b. Glasgow
Robert Buchanan 7 b. Glasgow
Allen Buchanan 5 b. Glasgow
Margaret Buchanan 3 b. Glasgow
John Buchanan 1 b. Glasgow
Janet McAllister stepdaughter 15 b. Glasgow
(I only have access to transcriptions of the Scottish census).
Jessie McAllister was, therefore, actually born as Janet Finlay on 29/12/1855 (not 27/7/1858) and in 1861 and 1871 appears as Janet McAllister. By 1881 Janet has become Jessie and marries as such that same year.
So, have no idea where the birthdate you have for her comes from. There was certainly no birth that matches this date and I hope I have proved to you from her marriage details, relevant census and birth entry that she was actually born 29/12/1855, and that although brought up with the McAllister name her parents were never married. (There was an Angus McAllister bc.1826 living in Glasgow in 1861 who was a Ships Carpenter so possibly a candidate for Jessie's father).
Annette