JSFiddle - React, Tailwind, and code Playground

HTML

<form>
    <select name="first">
        <option value=""></option>
        <option value="1">one</option>
        <option value="2">two</option>
        <option value="3">three</option>
    </select> 
    <select name="two">
        <option value=""></option>
        <option value="1">one</option>
        <option value="2">two</option>
        <option value="3">three</option>
    </select> 
    <select name="three">
        <option value=""></option>
        <option value="1">one</option>
        <option value="2">two</option>
        <option value="3">three</option>
    </select> 
</form>

JavaScript

$('select').on('change', function() {
   $('.select').next().trigger('click'); 
});