If there were to be an incident during flight, such as a toilet fire or something, then for us, it is the cabin crew who will deal with it. No flight crew are involved. If there is one on rest, if they wish to involve them self, then they will return to the flight deck to be involved.
In regards to evacuation or an incident on the ground, again, a third flight crew member would not really be involved in any official way. If you take a planned emergency landing, or unplanned for that matter, by the time we have either begun an evacuation in "clearly catastrophic situations", or have been commanded to commence an evacuation by the flight crew, we will either be nearly finished or quite a way into our 90 seconds evacuation by the time the flight crew have shut down the aircraft and area leaving the flight deck etc. Of course, once again, this is all dependant on the situation and how long the flight crew are able to stay in the flight deck before they must get out them self etc. However, saying that, once on the ground and out of the aircraft, I would expect that the flight crew would then be involved in managing the passengers on the ground in any interim period till enough emergency services capacity were at the scene to take over the management of the passengers once off the aircraft.
As we are reminded during our training, the first wave of emergency response to an incident on an airport, will be there to tackle the fire/other immediate situation, and the management of the passengers and crew will be done once the immediate threat of fuel fire/explosion has been dealt with or is suitably under control, and ultimately, it would be up to us to manage the passengers. Of course, as has been seen in multiple incidents with the increased use of camera phones and the likes, that this rarely happens as people will scatter over a wide area once off the aircraft, and to be frank, if we were taking the full amount of time to evacuate the aircraft, we may not be on the ground with them till a full 90 seconds after it started, and by that time, they are not going to be within an area to listen to our instructions, nor take any notice.