The automatic follow-me functionaility originally was designed to work with mobile orbiters that used bluetooth to connect. When it lost a connection in one room and picked up another one in another room - it assumed that you had switched rooms and would get the currently playing media to follow that user. If the media director is busy I am not sure what is meant to happen.
There are various posts on the success (or not) of this implicit follow me.
What does work (and reliably) is explicit follow me, where the user tells an orbiter where they are and what media to move where. This is can be done using any orbiter and using a floorplan of the house. This certainly works, although I had had different levels of results depending upon the media type. Some types seem to restart, some try to continue but get it a bit wrong. It certainly is a great feature though and makes you feel very powerful
It also enables the same media to be easily streamed to multiple spots.
The fiire remote also has an explicit feature which I think works similar to a mobile orbiter, but rather than automatically detecting a user moving it waits for the user to press a follow me (connect) button on the remote. I understand that this works very well.