Throwing my hat in on this being an issue as well. Can confirm it's only impacts that count towards damage done. In the attached video I show my challenge has 170/2000 damage done. I then shoot the airburst next to someone, doing 61 fire damage. My challenge progress done doesn't change. I then direct impact someone with the airburst, doing a total of 42 damage, and my challenge increases by 14 (184/2000).
Further showing it's impact damage only is how people have been completing it thus far: Spawn as Engineer, put a mine next to a vehicle. Redeploy, spawn as support with Airburst, use airburst to shoot the mine causing it to blow up and do 1000 damage to the vehicle. Your challenge progress will increases by 1000.
