Party A is the original caller.
The type of transfer you are describing is a features transfer. As you don’t seem to have configured the features, it is a blind transfer, which will, obviously make the announcement to the parkee, as the transferror is out of the circuit the moment the parking extension starts running.
If you want the transferror to hear the announcement, you will need to perform an attended transfer (I can’t guarantee that features transfers work this way). However, there is also a specific feature code for parking, although I’m not sure which party it parks. see configs/features.conf.sample.
Moreover, if you have a proper SIP phone (the free version of X-lite has this disabled) you can use the transfer command on the phone to transfer to the parking extension. If you use the attended transfer option, you effectively start a call on a second line, and only associate that call with the original caller after you have finished parking it.