The continue shopping button generally goes back to the last viewed product's product detail page. To get a button that will link to the product results page, you could create a form with a button that posts to the products results page.
<form id="continueShopping" name="continueShopping" method="post" action="Products_Results.php">
<input type="submit" name="continueShopping" id="continueShopping" value="Continue Shopping" />
Then you can style the button the way you want.