Sounds like you might need to increase the local preference on the new registrar.
OK, back to being serious, they don't announce to the root server. The registered nameservers (belonging to the registrar in your case, but in many other cases belonging to an ISP/NSP/WHP) answer queries made by the resolvers of millions of happy end viewers. The TLD servers (a level below the root servers) will at some point begin referring questions about your domain name(s) to the new nameservers (belonging to the new registrar). Some of those resolvers out and about the Internet will have cached the reference to the old nameservers for 1-2 days, but will eventually forget that and be told to ask the new nameservers.
Try the O'Reilly book on DNS and BIND; the mud will become clear as spring water.
IP Network Engineer