Unfortunately in DomiNations, my experience is that the building doesn't have to be trapped by walls, just behind them. So after you breach the outer wall, if you drop another miner right away it will just go to break another hole in the outer wall.
Whenever I've tried dropping two miners right away, they just end up targetting and blowing two holes in the outer wall. It seems like the second miner doesn't notice that the first wall is breached so he never goes for a deeper wall. Another issue is that a ballista or tower on the other side of the wall might target them if they ran out in front of the other troops. So depending on the base you might have to actually wait until the whole outer layer is cleared before dropping the second miner.
One minor (miner?
) annoyance is that they won't attack a wall
unless there's a building behind it. This comes up when you've cleared out the inside of the base and you're trying to get through the far wall to get to the last outside buildings. You'd think a miner dropped out there would be happy to blow a hole, but if the inside of the base is empty the miner will instead target a nearby building with his axe.