According to this source a Battle Event is a one of the following:
- Skirmish between at least 2 players
- A huge battle between at least 2 armies
It happens often after long passive (peace) phases and it can happen only 3 times. The attacking party / aggressor gets the Battle Event, this is why Yellow does not have a Battle Event.
In your example the 3 Battle Events for orange and green are over. Furthermore a Battle Even occurs when the armies first clash, so if you overrun your enemy in say 5 minutes then only the first "encounter" is considered a Battle Event.