Mostly the instant access url is to help you test the site in it's new location before executing the actual move.
Since september, DNS changes for .com and ,net have been taking 15-60 minutes to propagate in the US. One hint is to put some unigue identifyer on the home page of the new location - like a small x at the bottom of the page - so you know where you're winding up when you go to the site.
I would still leave the old site up for a few days to allow for world-wide propagation of the new location.
If you're using sql server, and you have an ip address for it in the new location, you can run both sites pointing to the same db in the new location.