Yes, that is wrong! Well, it's "sub-optimal", shall we say...
Once your new hosting account is activated, they will give you an IP address, like [127.0.0.1...]
You can use that to upload your site contents to your new host.
After that is done, you (or your new hosting company) should contact your domain registrar, and have them update your DNS (Domain Name Server) record. The DNS record says, "hollyhats.tld" means 127.0.0.1". Therefore, anyone who enters your domain name in their browser gets connected to your new server.
Since the numerical address doesn't normally show up in links, most folks are unaware that they could also use a numerical address to get to any site if they know the number. Domain names are just a convenient way to name sites, since most humans would have trouble remembering all those long numbers!
It will take several hours to several days for the new DNS record to propagate to DNS servers worldwide. During that time, some visitors will connect to the old server, and some will connect to the new server. Companies like Google - who keep their own DNS information - may not update for several months. That's the reason for the advice you see here on WebmasterWorld recommending that you keep the old site on-line and keep it updated for awhile.
Since you are a new customer for your web hosting company, you should ask them for help if any of this is unclear or if you just can't get things done. They have a vested interest right now in keeping you happy, and will probably help you out.
Hope this helps,