We use tea tree oil based cleaning products in our house, and personal cleaning productions and lotions. We've never applied any directly to the cats.
Everyone's doing just fine, far better than the cats would be doing if we used toxic chemical cleaners.
I used a tea tree oil based lotion on the burned pads of a small dog once. His owner did not realize that concrete and asphalt are just as hot to dog feet as to bare human feet... Soothed his feet so much that he was back to normal the next day. But it was not straight oil, being diluted in the lotion.