For filling litter boxes/hay racks, I’ve found that it is impossible to not get the stuff everywhere. BUT, it sometimes helps to “twirl” the hay in your hands like spaghetti to keep it from being too loose while you transfer it from bag to bin. I pull a handful from the big hay mass (with my hands still inside the bag to keep it from going everywhere) and roll it around itself a bit before taking it out and putting it in Olaf’s hay rack. Not only does this help keep flyaway from falling everywhere but I think it helps keep the hay in the rack better since it clings to itself rather than being loose and falling out the bottom.
But there are still bits here and there. The first few times I used the big vacuum I put Olaf in the other room in his carrier, worried he’d be horrified. He didn’t seem to care so now I vacuum while he’s out and about and he either hides in his diggy box or is brave and walks right up to the big scary monster machine to sniff it.