Hello supercain2. Often this type of behavior occurs because of caching. This is especially true if the servers have different DNS.
There are generally 3 types of caching that may be involved–your computer’s dns caching, your browser cache, and serverside caching.
Because you don’t tell us what browser or operating system you’re running, it’s very difficult to provide instructions. You should definitively clear any serverside caching you may have in place, either via a WordPress plugin or through facilities like Memcache or Redist.
If the site changed DNS, then sometimes it’s just a matter of waiting for the computers around the world to get that news and the situation will sort itself within a few days at most. It might be helpful to go to a DNS resolver site like Google (https://dns.google.com), enter your new URL, and see if the DNS resolves.
Each browser has its own particular set of instructions to clear the cache–the keyboard shortcut ctrl+shift+delete works on many of them.
Sometimes your computer caches DNS queries as well, and these need to be cleared in order to get the new site. That’s usually done either via an IPconfig or IFconfig command, as in ipconfig /flushdns. But again, it differs between operating systems.
You should also consider doing a search-&-replace of your database, making sure that your old URL is replaced w/your new 1. Back up your database prior to doing so, please.
If you’re using any type of caching plugin, then please ensure that all caches are empty. Also clear any serverside caching that might be in place.
DNS can be a tough subject to understand, so don’t hesitate to ask if you have questions. Actually, caching can be a tough subject as well, so please ask if any of this feels hard.
Please let us know.