Is tea tree oil still toxic to cats after it has dried?

I don't think I asked my last question right. I have three indoor cats that stay on my porch while I clean. I usually use tea tree oil to clean because I am allergic to a lot of commercial cleaners. I realize, and have known, that tea tree oil is toxic to cats if used topically or ingested, especially undiluted. I use a mixture of water and tea tree oil, 3 drops of oil to every 3-4 cups of water. I'm afraid that, even though my cats do NOT come into contact with the oil or mixture wet, the residue left over on carpets and floors after it has dried will harm my cats. My windows are always open when I clean with the oil and I always wait at least an hour (or until everything is dry) before I let my cats back inside. I'm afraid of the long term affects the oil may have if it can be absorbed into the paws of my cats after it has dried. Does anyone know if tea tree oil still toxic after it dries? Sources would be greatly appreciated!

Thanks!!