When adding a participant to a conference in the Aircall app or Aircall Workspace, you can choose to conference with a Teammate, saved Contact, or manually enter a number.
When you transfer a call to a saved Contact or external number, a new outbound call will be generated that is separate from the ongoing call where the conference was initiated. These outbound calls are part of the conference but they won't contain call recordings. Instead, the recording for the conference call will be tied to the main call.
For example, here's a conference call in the app History where the recording for the conference will be located under the main call:
The result is similar in Aircall Workspace where the recording is available on the main call and not in the separate outbound calls to new participants: