I checked online trees and found the following:
The 1900 Census record for his daughter, Mary Oldman nee Smith, states that her parents were born in Ireland:
"United States Census, 1900", database with images, FamilySearch (https://www.familysearch.org/ark:/61903/1:1:MSXX-G8H : 22 January 2022), Mary Oldman in entry for William Oldman, 1900.
Scotland Census Records for John Smith that are attached to him on Ancestry trees state he was born in Ireland (I used the citation maker, you can copy and paste these if you need them):
1851
* '''1851 Census''': "1851 Scotland Census"<br/>Parish: Irvine; ED: 3; Page: 3; Line: 8; Roll: CSSCT1851_132; Year: 1851; Household Schedule Number: 7; Roll: CSSCT1851_132<br/>{{Ancestry Record|1076|2586850}} (accessed 2 October 2022)<br/>John Smith (22), Coal Miner, head of household on Bridgegate Street, Irvine, Ayrshire. Born in Ireland.
1861
* '''1861 Census''': "1861 Scotland Census"<br/>Parish: Irvine; ED: 2; Page: 33; Line: 1; Roll: CSSCT1861_85; Registration Number: 595; Household schedule number: 225; Roll: CSSCT1861_85<br/>{{Ancestry Record|1080|3000104}} (accessed 2 October 2022)<br/>John Smith (33), Dealer In Polataes, head of household on Bridgegate St in Irvine registration district. Born in Ireland.
1871
* '''1871 Census''': "1871 Scotland Census"<br/>Parish: Dundonald; ED: 7; Page: 11; Line: 22; Roll: CSSCT1871_110; Registration Number: 595; Household schedule number: 74; Roll: CSSCT1871_110<br/>{{Ancestry Record|1104|504893}} (accessed 2 October 2022)<br/>John Smith (45), General Dealer, head of household in Halfway in Irvine registration district. Born in Lanoy, Ireland.
I don't know where Lanoy is in Ireland or if the spelling is accurate.
I can see that the WikiTree profile for her mother also states that there is uncertainty as to whether she was born in Scotland or Ireland.