I watched replays of a recent ATG vs. VBN game. Alex faced a situation where he really wanted to break the block on the Barbarian secondary town but didn't want to lose his archers. So, the chain of heroes redirects to another target, and the block on the secondary town is taken later, already with cavalry in the army.
That is, there isn't a task to attack everything indiscriminately, regardless of the cost. As the map unfolds, objects of increased attention are identified: the secondary town, the stable, the refuge, and the +3 Luck/Morale amulet. And the chain of heroes adjusts to take them all. But the amulet is postponed until the second week, and the block on the Barbarian town is delayed until reinforcements arrive. And before that, other targets are captured. That's the impression I got.

Sorry if something is wrong; my analysis of replays is not perfect.