I know for a fact that Dettol is extremely toxic and usually fatal to any species of cat/felines, as their bodies cannot eliminate the chloroxylenol. So people who have a pet cat should not EVER use Dettol or any other product that contains chloroxylenol anywhere in their homes, their cars, etc. where their cat could ever breath the air or come in-contact with the surfaces that it's been used on.
Dettol has also been found to usually be toxic to marine life, although not quite as toxic to fish/marine life as it is to cats.
If you do any research about chloroxylenol and birds, what you'll typically find is something that says that "Chloroxylenol is practically non-toxic to birds"...that's me summing-up what the research states.
Basically the bottom-line from everything that I've read is that Dettol is usually not toxic to birds, but it CAN BE toxic to birds and HAS BEEN toxic to birds, in both surface-contact and mostly respiratory/air contact situations; the fact that Dettol has been found to be toxic to birds the most through respiratory-contact makes sense, as birds obviously have extremely sensitive and complex respiratory/air-sac systems...
For me and my birds, anything that has proved multiple times to be toxic/fatal to birds is never, ever worth the risk, as I fully know that the product/substance has and does kill birds, no matter how often it happens, it still happens. When there are many products/substances that are completely non-toxic to birds that you can use instead of Dettol, the best thing to do is to not ever use it around your birds, or in your home where your birds are, regardless of what room their cages are located.