How to refresh order review at checkout via ajax?

In my WooCommerce plugin, I’m using devbridge autocomplete plugin for shipping city field. And after the city is selected, I want to refresh order review via ajax.
Here’s the JS:

jQuery('input.city-search').autocomplete({
    serviceUrl: ajax.url,
    paramName: 's',
    params: {
        action: 'wp_ajax_city_search'
    },
    transformResult: function(response) {
        response = jQuery.parseJSON(response);
        return {
        suggestions: jQuery.map(response, function(item) {
            return { 
                value: decode_html(item.text), 
                data: item.data
            };
        })
    };
    },
    onSelect: function (suggestion) {
        jQuery( 'body' ).trigger( 'update_checkout' );
    }
});

The problem is that jQuery( 'body' ).trigger( 'update_checkout' ) just does nothing.
I tried $( document.body ).trigger( 'update_checkout' ) as well, but result is the same – nothing. I tried to check if there are any events bound to body – jQuery('body').data('events') and it has shown that there are none.

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