These 6 are all definitely the same family- children of James Fullerton (schoolmaster) from Tullygarley in Ballymena.
Does your John fit in here as one of the younger sons in the family?

Robert John Fullerton born abt 1815, died 1873 (weaver); married 1847 Ballymena to Margaret Connolly.
Note: his marriage record gives name of father as
James Moore Fullerton, schoolmaster.
links to Renfrewshire, a son named James born abt 1853 married 1881 Eastwood to Margaret Mailey at 36 Herriott St Pollockshaws. He is in Eastwood in 1891 census, and died Eastwood 1904. Another child Mary Ann Fullerton born abt 1852 is in Herriot St Pollockshaws in 1881 census with her sister Margaret (Fullerton) Gault born abt 1860.
Mary Fullerton born abt 1818; married 1850 Ballymena to William Stewart (weaver) -
marriage witnessed by William Orr and Alexander Fullerton
Agnes / Nancy Fullerton abt 1820 -1875; married 1846 Ballymena to William Orr (weaver).
Robert J Fullerton is a witness on the marriage links to Renfrewshire and calico printing through daughter Agnes Johnstone (as per your post)
There is also a son named James Orr (1847) who is in Dumbartonshire in 1891-1901 census. He died 1928.
James Fullerton abt 1822- 1878 (weaver) married 1849 Ballymena to Margaret /Martha Thompson.
William Orr witness to the marriage
Alexander Fullerton abt 1825-1879 (weaver) married 1848 Ballymena to Agnes Rea
links to Renfrewshire and calico printing through his son, and his 6yr old grand-son who is with your John Fullerton in the 1891 census.
Sarah Fullerton (born abt 1826 - 1904) married 1848 Ballymena to John McMeekin (bleacher/ dyer) who died 1883 Eastwood.
This couple are in Thornliebank Eastwood, Renfrewshire as early as 1871 census, working in the textile indsutry.
https://www.freecen.org.uk/search_records/5b91a7d7f4040b176c900761/sarah-mcmeekin-1871-renfrewshire-eastwood-1832-?locale=en Looks as if Sarah (Fullerton) McMeekin died in Eastwood in 1904 on death index her mothers name shows as Miller. Not McMillan

, but name may not have been remembered correctly by whoever was the informant. The other possibility is that her father James had more than one wife. First wife Letitia McMillan and second wife Sarah Miller. This might explain why the name Letitia is not present in offspring of all family lines this is the only aspect that gives me some cause for reservation.
[
Sarahs death rego might be useful to see what it says about parents. It might support or cancel my theory about 2 wives for James F]