When destroying the structures, the minions don't actually do anything, but they are slowly chipping away at it so long as the enemy isn't defending it as well. If they're in the red/blue square in front of the structure (or ring for crystals) they should be doing something.

The shield though, in my experience, takes a long time to destroy. The best way to destroy it is with a groups special, I think the Red Panda is what I've been using; Four of those together, power up their special, and it knocks 70% off the shield, done again and the shield is destroyed.