The caller ID is sent to the phone before it starts ringing.
When you make a SIP supervised transfer, the phone starts a completely new call, with its caller ID, so the phone indicates a caller ID just the same as for a non-transfer call from that phone.
When you complete the transfer, the phone sends a message saying please subsititute the connection that it has made to the callee for the connection it currently has with the caller. Only at that point can the PABX reliably associate the two calls. That means that there is no way of indicating the caller to the callee until the transfer is completed.
However, what looks like one call through the PABX is actually two calls; one to the PABX and one from it. The calls that get reconfigured are the ones between the operator and the PABX. There is no change in the calls between the PABX and caller or callee, so there is no opportunity to update the phone number.
For a res_features transfer, Asterisk is more aware of their being a transfer in progress, so the behaviour may be different.