Here's something to be aware of when transferring domains:

Just because you have transferred your domain does not mean you have transferred the zonefile - the file which contains info about where hostnames and MX records resolve.

Typically the process goes something like this:
Step 1. Transfer the domain ( you can read more about this in the FAQ )
Step 2. Recreate the zonefile for the new name server.
Step 3. Update the auth name server for the transferred domain
Step 4. You have successfully migrated from provider A to provider B

So, if you're thinking about transferring your domain and hosting to another provider be aware of the steps and, as always, if you have questions about the process be sure to ask about anything that you don't understand.