If the players aren't in the Ark, the GM do the Ark stuff as he see fits (according to the rules in the textbox on p103).
This can be very interesting. In a campaign I had a couple of years ago, the Ark was attacked and was in desperately need of better defence. The players knew that but they got a lead to a bunker, a bunker that could hold some leads to Eden. This bunker expedition took several sessions before they came back to the Ark. When they came back, the (GM controlled) Assembly had finished Militia (started by PC), Tribunal (started by PC). but also Surveillance because there was rumoured that the Ark has a traitor (working with the attacking group), a Torture Chamber was started and finally Autocracy was started. One of the bosses (despot) has managed to scare the people so much that they have started to believe that what the Ark needs is a strong leader. That become an interesting situation for the players to deal with