Hypo allergenic doesn't equal no allergies, just less likely. You can still be allergic to natural products, too. I found several references to people having atopic reactions (skin allergies) to yucca plants, so it's possible that your little guy is, too. A veterinary dermatologist referral would be a good idea.
It's also possible that he is sensitive to the cleaning products they use on the equipment.
ETA: This site says that Yucca is toxic to dogs. Not sure how reliable it is, but it's worth looking in to.
http://www.dog-first-aid-101.com/tox...en-plants.html