I find that odd actually; eucalyptus contains an oil that quite a few people are allergic to. I’d never heard it was a rare allergy, in fact, elements of its oils are often associated with allergies:
Yeah, essential oils are pretty potent. As are the delusions some folks have about them.
The leaves probably have the highest concentration but there's oil throughout the whole tree.
In reading on how the Tencel is made, it doesn't appear that they do anything special to remove oils, just making sure the fibers are flexible and "dry."