It doesn't actually move your cursor, just an image of a cursor. You should be able to copy & paste the URL out of your address bar as it is animating; you're r

It doesn't actually move your cursor, just an image of a cursor. You should be able to copy & paste the URL out of your address bar as it is animating; you're right that just showing the URL after the user clicks 'Search' might be more user friendly, though.