The index on Scotland's People lists Mary as Mary Stewart Ward so maybe the couple never married. As you say the list allows limited search criteria.   
In 1901 the only James and Mary Ward I can see (with James a coal miner) are living at New Cumnock, Ayrshire, as below but there is no Thomas and the age of Mary is out 
Edit and in 1891 they had no Thomas
WARD, James 38 Coal Miner b Irvine, Ayrshire    
WARD, Mary 37 bIrvine, Ayrshire     
WARD, John G 10 b Irvine, Ayrshire    
WARD, Jeanie H    8 b Irvine, Ayrshire       
WARD, James 6 New Cumnock, Ayrshire 
WARD, Mary H 3 b New Cumnock, Ayrshire 
WARD, John Brother    Married 34 Coal Miner b Irvine