They might have built special very armored freighters with meson bombs in it, ready to be deployed next to every single GTVA node (or -somewhat- near any space station next to the nodes). They might have created a "Meson Protocol" ready for action, the moment the Shivans start to appear again.
Other kinds of freighters specially designed for quick evac from planet annihilation might have been also built. The "Meson Protocol" would comprise of both the placement of the bomb, the coordination of these special evac freighters that could be (perhaps) stationed in multiple places around every planet ready to take off at all times, along with all the emergency management of all the people in the planets for really fast procedures.
Instead of taking hours, days for evac, a designed procedure with lots of resources poured into it would minimize the time to several minutes, perhaps one or two hours before all the evac freighters are leaving their planets. Not only the populations would massively require some sort of this kind of planning, the military would also pretty much want this to happen, for the losses suffered against the Shivans trying to slow them down while the populations evacuate in the events leading to the Cappella incident were tremendous.
edit: wait, I read the title and realize, this is extremely off topic!! Sorry