Not really important to fix, but I figured I'd post a report anyway so you're aware of it. Seems like being inside one of these factories changes the LuaEntity owner and screws with your code. Error is below:

LuaEntity belongs to surface Factory floor 1 (index 1) but a LuaEntity belonging to surface nauvis (index 0) was expected. stack traceback: TheFatController/GUI.lua:21: in function 'start_following' TheFatController/GUI.lua:794: in function 'toggleFollowMode' TheFatController/GUI.lua:315: in function <TheFatController/GUI.lua:302> [C]: in function 'pcall' TheFatController/GUI.lua:302: in function <TheFatController/GUI.lua:301>

Yeah, you caught FAT not being made for multiple surfaces. I hoped i could get away with it :D

I guess a quick fix is to just make buttons not work when the player is on another surface.
Proper support for surfaces will probably take a while (low priority since this is the first time a bug with surfaces is reported)