I don't remember exact times but I have the same experience as you did: when I logged at morning, no event was running, I completed all missions.
Then I've logged in later in night, event was running, the event mission was still not there.
Based on my experiences in programming, I suspect they started the event late and only people who didn't logged between the "end of day" (the reset which happens at 3:00 GMT if I'm counting correctly) and the start of event saw the event mission.