All that I can tell you is how I would have it done since I would want a measure of control. I would and have been seated next to the web designer as he pulled out the old site and installed the new one either on my company's server or on the hosting service's server. Then, we would go through all of the facilities using a laptop as if we were viewing the site to test out if everything works. That's with a web designer who is either my employee or an independent contractor working for me because I know that he wouldn't mess things up. If he did make a mistake he could fix it on-line in a few minutes with me there.
Another way is to keep the old site up and running until final testing of the new site is completed on a dummy server. If everything works, then the old site is taken down and the new one is installed on the actual server. This is what is probably happening with DGRI's contracted web designer.
If the host computer is through a service, then things become more difficult than hosting your site on your own company's server. My corporate site is on my company server and not through a service provider. It's much simplier and we keep control.
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