The invasion needs to be cleared in a relatively short period of time, typically requiring multiple people to do it, in order for this quest item to spawn. It was late at night so I was trying to clear it alone and I didn't understand why the item wasn't spawning, but it's because the invasion will end if it's not cleared fast enough and not give the item. I had to switch war mode off to have enough people around to clear it. The item spawns with a blue exclamation mark towards the middle of the camp and will be hard to miss. As someone else commented, the quest item stays spawned for 5 minutes and does not require participation in the raid, so if you have multiple alts logged at Brewfest you will have time to switch through all of them and pick up this quest. Also, the invasions take place every half hour exactly on the half hour and hour (i.e. 7:00, 7:30, 8:00).