Any time that DNS changes are made (on any level), you need to wait for propagation to complete. Propagation usually takes from 3 to 5 days, but can take as long as 7 to 10 days. During propagation, traffic may come to either location. One person may see the new server while someone else sees the old one. Also, "yourdomain.name" may work while www.yourdomain.name does not. All of this is normal during propagation.
Please note that this means that just because you go to the new site when you type in the domain name does not mean that propagation is complete. The best way to determine whether or not propagation is complete is to review the statistics for each site (both the old one and the new one).
Detailed explanation of propagation:
DNS stands for Domain Name Service. Every time you go to a website using a domain name, you are using DNS. Your request for "thatdomain.name" goes to your local primary or secondary DNS server (which is usually administered by your ISP). Your local DNS server checks its records to see if it "knows" what IP address that domain points to. If it does, then it directs you to that IP address. If it does not, then it sends a query to the Root DNS servers.
The Root servers are what makes the process work. When a domain is registered, it is added to the Root servers. When a domain is expired, it is removed from the Root servers. The Root servers tell your local DNS server which DNS servers ("out there") are Authorative (are the primary and secondary DNS servers) for your domain.
Your local DNS server then queries the Authorative DNS server, and the Authorative DNS server tells your local DNS server what IP address the domain is located at.
Your local DNS server then caches (makes a copy of) this information. This caching process is essential: not only does it speed up future queries, it also reduces the load on the Root servers. It is this caching process that leads to propagation.
Your local DNS server does not keep that information forever. Instead, it keeps the information for a certain amount of time, at which point it deletes it. The next time that you try to visit that domain (after the information is deleted), the process starts all over again.
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