Put explicit tabindex attributes on your select form elements, such as:
<select id="mounth" tabindex="2">
In your script, in the $('select').each(function(){...
Add this:
tabIndex = $this.attr('tabindex');
And modify the line where you insert the styled div version to include the tabindex attribute with the original tabindex number that you have captured with tabIndex:
$this.after('<div class="select-styled" tabindex='+ tabIndex +'></div>');
That should give you what you want.
(Here's a revised page of your codepen page with it in action: http://codepen.io/anon/pen/rIeHd )