Hi,
where you have this in your template (call to show ajax search):
echo do_shortcode('[yith_woocommerce_ajax_search]');
just replace with above code:
echo str_replace(".autocomplete", ".yithautocomplete", do_shortcode('[yith_woocommerce_ajax_search]'));
Also you can find here more info regarding php str_replace function…
P.S. I’m using paid version of this plugin but i think this above will solve issue on free version…