I got to go to the Montreal Insectarium and they had an Atta leafcutter display. So I took some pictures. Whatever lighting they had, my camera did not like, so the pictures aren't the best.
I didn't get to talk to the main keeper, but I did manage to find someone who knew a few details.
The containers are not connected, and the ants can be seen carrying brood between chambers occasionally. There is a 5" tall barrier of fluon, and a water trap to catch those that escape. There were enough in there that I was surprised.
They don't water the nests, the ants bring in enough plants and water to maintain humidity.
They have neat little leave holders on the tree, to which they add new green stuff every day.
They remove a lot of ants and a bunch of fungus every few months to keep the population in check.
They aren't always the smartest, as indicated by the picture of the one ant obsessively trying to get a large piece of leaf into that narrow tubing. Another ant eventually came and cut it up so it fit. All garbage was drug to the far corner.