Is tea tree oil safe to use to clean around cats? Please read details.?

I use tea tree oil to clean my house since I'm allergic to most chemicals found in cleaners. I know that if ingested or put directly on cats, tea tree oil can be fatal. I have three cats indoors. When I use the oil, I always leave the windows and doors open, since it has a strong smell. I also put the cats out on the porch so they don't get into it. I'm just afraid that they will absorb any residue through their pads or that inhaling it will hurt them when they come back in later on. I use a mixture of 3 drops of oil to every 3 to 4 cups of water depending on what I'm working on. Any suggestions? Again, I know that tea tree oil can be fatal if ingested or applied topically. I'm only concerned if a residue will be left over (hours later) that will harm my cats. Especially in carpets and vinal floors. Thanks!