Seems odd that the wife's name was not mentioned on this. Did it mention his daughter by name - Poor Relief Applications usually mention the place of birth of children, often by street address...According to poor relief record in 1890 he was married and living at 4 Duncan Street Calton. It doesnt give wifes name.
I'm just trying out different angles as I can see no obvious sign of your young Matthew on SP either. I wonder if they were not married and the two children we think are theirs, Annie & Matthew, are registered under their mother's surname, which, of course, we don't yet know?
Looking forwards in time with that Mat*thew..there are only three marriages on SP for a Mat*hew Casey - in 1918 Glasgow, 1922 Renfrew & 1924 Glasgow. If your Ma*thew is good enough to provide us with the names of his parents, that might help, though he may have left the country and maybe none of them are him....
Best wishes
Lesley