Your third trigger's event deals with a destructible, so the game cannot recognise [triggering unit]. I don't know if there's a way to detect a destructible's destroyer, so imo just make a dummy unit that's a barrel and use [killing unit] instead in your third trigger.
PS: Tiggering Unit is the A Unit in your event triggers. Look at your second trigger, 'A unit enters Bloodwing commander spawn', the A unit is your triggering unit (it's also the Entering unit, but with triggering unit you can use waits).