Question is, did the cat "back wash?" haha

I usually use deionized water for misting as it has less mineral content compared to tap water that has been dechlorinated. I think this is how its best done...someone else can chime in.

This way you don't have mineral deposits on the glass/plastic walls. However, do use the dechlorinated water for ponds and water dishes as it's better for the frog/critter since it has minerals in it. A lack of minerals will cause minerals from inside the frog to move to where there is a low concentration (the water) and over a long period of time you'd be robbing your frog of it's micronutrients.