I don't do anything to my established hives. They are on their own after the first year.
Are you saying you don't manage your bees at all? You just take care of them the first year, and then do nothing? If that's the case, any management plan would fall on deaf ears. If you are managing them, then I don't understand your post.
So, are you saying that I should have gone in and taken brood or resources, if I had made the judgement that they were 'strong' in early July? Are you saying that I should go in and weaken them, to some extent?
The methods that FRAMEshift said are good examples of things you may consider. Some prefer to checkerboard, others to open the brood nest, others prefer the MDA Splitter technique. The jury is still out as to which one I prefer, I havn't had too much experience with any one method to claim it's my favorite.
Others choose not to manage, and when they produce swarm cells, the just create splits. Or even still, split them before the swarm cells start. Those are options as well.
And still others may choose to just let them swarm, capture the swarms you can, and move on from there.
All of the above work well with spring swarms, but the strategy is different for fall swarms (or late summer). Since those swarms are smaller, and don't have as much time to build up before the winter, they often can't survive as a stand alone hive for very long (unless you have a large late summer flow). For that reason, I've found letting them swarm is the worst option. It weakens both hives, reducing chances that the swarm or the old colony can make it through the winter. Waiting for the swarm cells and producing splits can have the same disadvantages.
But, if the hive is strong enough to do a split, do it early before they are ready to swarm. You'll have better chances overwintering both hives than you would letting them grow big, swarm, and try to get half the colony through the winter.
Does that make it a little more clear?