I got a reply from Logitech customer support:
"Thank you for your recent inquiry about your Harmony Remote.
I understand your concerns. Please use the following steps to ensure that the Adapter is paired correctly. The Adapter was designed to not interrupt the usage of your Original Gamepads. When you attempt the following pairing process please ensure that all of your Gamepads are ON also.
Answer Title: Pairing your Logitech Harmony Adapter for PS3T to your PLAYSTATION©3
Answer Link:
http://logitech-en-amr.custhelp.com/cgi-bin/logitech_en_amr.cfg/php/enduser/std_adp.php?p_faqid=11490&p_created=1238786194
If you would like further information and other tips on customizing your remote please visit the FAQ portion of your Harmony member website. To access, Click Support, then click FAQ while logged in your harmony member page.
We hope that we were able to assist you in resolving this issue, however if you are still experiencing any difficulties with your Harmony Remote, please feel free to contact us again."
I'll try pairing the game controller & the adapter again & see what happens.