What you did was sanitize the cage. Not treat it for mites
The way the "cage treatment" works is by taking the water bowl out of the cage (or tub) as well as the snake, but leaving everything else in. You then spray LIGHTLY.
Its been about 10 years or so that I had to treat a tub, so I'm not sure anymore how much you spray. But it was not much at all.
You then let it dry. (doesn't take long). After dry, you put the water bowl AND snake back into the cage. As the snake slithers through the cage, it comes into contact with the "stuff", there is a light coating all over and that seems to be enough to kill the mites in the enclosure and on the snake. It seems to be somewhat in the "air" as well.
I remember it was important not to go overboard with how much you use and it was important to leave the snake and water OUT until everything was dry.
That is the "cage" treatment. Those sprays contain permetherine's . Which is safe, as long as you use it exactly as you should, and also don't double up by using different products at the same time, esp. if they use the same ingredients.
With that method you use nothing directly on the snake, yet it seems to work wonderfully. And it keeps working for a while , so no need to re-apply often.