It is not a remittance transfer. The reason is because the definition only covers transactions which are originated at your institution. In your example, your institution is the receiver, not the originator. In addition to being originated by your institution, the transaction would also have to be for personal, family or household purposes...
(g) “Sender” means a consumer in a State who primarily for personal, family, or household purposes requests a remittance transfer provider to send a remittance transfer to a designated recipient.
See Reg E Subpart B (section 1005.30) for all of the definitions that relate to these new requirements -
http://www.bankersonline.com/regs/12-1005/12-1005-000.html