What is your topology for this ? Is there a chance that the Refer CSS does not include the phones you are transferring to ?
Have you attempted to run RTMT to do a session trace to to the phone being transferred to?
If you can provide a topology and some logs we should be able to help more.
If Unity is using SIP, you need to ensure the REFER CSS is set as that is whats used when a transfer happens in unity.
I have the similar kind of issue. The unity call handler unable to transfer the calls to third party SIP phone registered with CUCM. The third party SIP phone is playing the IVR for speech assistance managed by Nuance. When I call the third party phone directly it is working fine. But call handler option 3 takes times and then transfer the call to operator(which is option 0) instead of option 3 third party SIP phone. Tried all possible troubleshooting but could not find the issue. Kindly help when needs to be tested further.