When the bees start filling the hive with nectar, they usually will fill the brood area with honey first. There still is plenty of brood and eggs in the brood box, but the bees pack in the brood area first. As more nectar comes in, and there is no where left to put honey, it is at that point, the bees move into the supers.
For the bees, it is about survival. They will fill their living area first, so there is honey for the future survival of the colony.
Beekeepers always blame queen excluders for their problems with honey not being stored in their supers. This really is not the case. I know a commercial beekeepers who runs 9000 colonies. He uses queen excluders on all his hives. He sees value is using excluders. Most beekeepers with more than a couple hives use honey robber with fume boards to remove their supers. Honey Robber is a odor repellent and makes bees leave the supers quickly.
If any brood gets laid in a super, the bees will not leave the brood no matter what is used. This make supers harder to remove and more labor is required to get the bees out of the supers as the bees have to be brushed off the frames by hand. If the excluders were causing him to get less honey, I am sure he would not use them.
Colonies with new supers and bare foundation, I usually suggest that queen excluders are left out until there is a little wax and nectar on a frame or two in the supers. At that time I would put in the excluder.
On my hives with drawn comb, I put the supers on top of the excluder and the bees move up into the supers when they are ready.
Excluders don't cause swarming. Lack of management by the beekeeper causes swarming. Beekeepers should still be on the seven day checking for swarm cell schedule. If this schedule is not followed, the bees may swarm.
If you are not getting any honey in your supers after a week or two of the start of the nectar flow, your hive may have swarmed or you are in a poor nectar area.
When a hive swarms the field bees leave. These are the same bees that will bring honey to the hive. If the field bees leave in a swarm, there are not enough field bees to produce excess honey and the hive is unlikely to have any honey in the supers.
How do you know if this has happened? If you look in the brood box and see no eggs or young larvae, probably some queen cells the hive probably has swarmed. Do not remove the swarm cells at this point, this will be your new queen. The bees may fill the brood area solid with honey as the brood hatches out.
Honey is coming in, hopefully you should see a a few full supers soon.