Problem with registrar, domain transfer

[cheyne]

am having a problem with several transfers I performed from one registrar to another, and I wanted to find out if this problem is normal behavior.

The receiving registrar is supposed to add 12 months of registration subsequent to transfer. Transfer has been complete for a week or more now but when I asked them why the 12 months hadn't been added their response was-

"Your domain is succesffully transferred but it might be possible that other registrar still not remove the domain from their account.
Please contact them to remove the domain. "

What does this mean? What should I ask the old registrar to do? I understood that a transfer was final and there were no lingering ties to the previous registrar...

Any advice would be appreciated.
Thanks