Interesting. I wonder if they use an undocumented AWS feature or are snapshotting the volumes and copying them. My guess is the latter.
http://elastic-security.com/2011/02/10/how-to-copy-an-ebs-ba...
http://serverfault.com/questions/336321/how-do-i-migrate-ama...
I'm 95% sure they are just putting a UI over that lengthy process. But as I say, I've tried it and it worked perfectly for me. This is their process:
http://blog.ylastic.com/migrating-snapshots-between-ec2-regi...