After going to the link you provided, I see in the docs that they have a rendering callback function, presumably meant to make use of your ajax responses.
Notice how I simply returned what I wanted the list item to contain. This may not be completely accurate, but you get the idea. look in the docs further for more information. (there doesn't seem to be a lot of documentation written, though.)
var render = function(term, data, type){
var link = "<a href="data.url.or.something">"+term+"</a>";
return link;
}
$('#search-input').soulmate({
renderCallback: render, //this is a reference to the function above.
url: 'http://soulmate.YOUR-DOMAIN.com/search',
types: ['type1', 'type2', 'type3', 'type4'],
selectCallback: select,
minQueryLength: 2,
maxResults: 5
});