Interesting read, I'm surprised these tubes are so fast considering my one remaining filament bulb always takes a few seconds to warm up after being switched on. Do these use a different filament type?
I think the filament stays on and you switch what cathode is being used.
edit, I just read the wikipedia page on nixie tubes, there is no filament, despite looking like one it is not a thermionic vacuum tube. it is a cold cathode gas discharge lamp. so one anode with many switched cathodes.