I guess you have to follow the event instructions first, since the usually begin with "At the beginning of this phase...."
The way I played my first (basic) game was to follow the instructions of the event card (usually spawning new zeds in some tracks) then activating the tracks stated. Is that right?
The event happens in the zeds phase and will say when it happens; if it says "at the beginning of this phase" it will happen right away befor you activate any tracks. If it says something else you trigger the event when the card says the event will trigger.