Do I install my green board before I install my shower pan?
Shower pan is always first because you want the top of the shower pan to the edge of the green board.  So there may be shimming involved to get the walls not only lined up with the pan but as close as you can to perpendicular.

I am not going to argue with your installers because I have had some large sheets of granite and marble installed for showers but I would recommend a backer board not green board.  Even if they say green board is fine because the water is impervious to their tile that doesn't mean water can't get on the green board from behind or up top.  And if they are gluing the sheets down there will eventually be issues.  Using Hardiboard would take water coming from any direction out of the equation.