Your widget responds to changes of an option

setWidgetOption.js

_setOption: function (key, value) {
    var oldValue = this.options[key];

    // Check for a particular option being set
    if (key === "className") {

        // Gather all the elements we applied the className to
        this.filterInput.parent().add(this.filterElems)

        // Switch the new className in for the old
        .toggleClass(oldValue + " " + value);

    }

    // Call the base _setOption method
    this._super(key, value);

    // The widget factory doesn't fire an callback for options changes by default
    // In order to allow the user to respond, fire our own callback
    this._trigger("setOption", null, {
        option: key,
        original: oldValue,
        current: value
    });
},