I got this working by keeping track of the "container" html element title attribute. And then adding an on change to that html element as well.
original code:
theOldText = $(".msos-selecteditems-container").attr('title');
$(".msos-selecteditems-container").on('DOMSubtreeModified', function(e) {
var theText = $(".msos-selecteditems-container").attr('title');
if(theText !== theOldText){
console.log(theText);
theOldText = $(".msos-selecteditems-container").attr('title');
}
});

guessing yours's will be:
theOldText = $(".new_referredby-container").attr('title');
$(".new_referredby-container").on('DOMSubtreeModified', function(e) {
var theText = $(".new_referredby-container").attr('title');
if(theText !== theOldText){
console.log(theText);
theOldText = $(".new_referredby-container").attr('title');
}
});