i am not sure if something in this note helps or not
amongst 111  McMinn listed in peoples trees on Genes Reunited are
George CharlesMcMinn   1869   Clonmel, Tipperary, ...   No   Lesley 
William   McMinn   1868   Don'T Know, Tipperar...   No   Lesley   
Alexander    McMinn   1861   Tipperary, Scotland ...   No   Lesley   
Alexander   McMinn   1860   Tipperary Scotland ...   No   Stuart   A
lexander   McMinn   1860   Clonmel, Tipperary, ...   No   Jennifer
Alexander   McMinn   1807   Tipperary, Ireland ...      No   Mary 
re GR British Army Service Recordsmore details about £11 each after you join
Alexander McMinn 1798  no birth locationEighteenth Regiment Of (Light) Dragoons
Alexander McMinn 1807 Kircudbright   GUNNER & DRIVER Royal Artillery
Alexander McMinn 1835 Burgh discharged Corporal Royal Artillery
Alexander McMinn 1860 Clonmel no rank
Alexander J. McMinn 1860 Clonmel no rank Royal Artillery Sergeant in 1891 census married living  in Folkstone Mary wife aged 20, Katharine aged 1 . Matilda Adelaide 8 months.  In 1901 Alexander john is living alone in New Monkland Lanarkshire  as 
Papermaker's Timekeeper Also Serving As Royal Reservist Sergeant 132nd Batt R F A, Also in 1901 Mary b maryhill  lanarkshire now has Elizabeth b 1892,  Alexander John b1894, Wm b 1896, and Albert b 1900
Alexander McMinn 1869 Cropmichael no rank no Regiment given
George Alexander McMinn 1881 Woolwich 1881 Royal Artillery