OK, census details.
1861RG9/2929 26 45
Manchester, Lancashire
10 Richmond StreetWilliam Hy Tyson, lodger, mar, 28, Blacksmith, b. France Cailas
Kate, wife, 20, b. Lancashire Ormskirk
Head of household is a John Moore, 29, Brewer.
1891RG12/3218 51 21
Salford, Lancashire
48 Durham StreetMartha Tyson, head, wid, 50, occupation: none, b. Lancashire Liverpool
Ada E Davidson, dau, mar, 22, Sticker?, b. Manchester
Martha Tyson, dau, 21, Maker up, b. Salford
Lewis? Tyson, son, 17, Miller, b. do.
William H, son, 13, scholar, b. do.
Emily, dau, 11, scholar, b. do.
1901 RG13/3730 53 25
Salford, Lancashire
46 Durham StreetMartha Tyson, head, wid, 57, b. Lancs Liverpool
Martha, dau, s, 29, Stitcher in Cotton warehouse, b. Manchester
Emily, dau, s, 21, (can't read occupation), b. Salford
Charles Brandon, grandson, s, 14, Errand boy, b. Manchester
Martin Mc Mahon, lodger, s, General Warehouseman, b. Ireland
Does Mary J's marriage cert really state her father's birth place? This isn't something usual
Have you made contact with the person who posted on the ancestry board?
If this William married to Kate is yours, then we don't know which children are Martha's and which may be Kate's, do we? A birth cert for Mary J would certainly be useful.