Not sure what you're looking for with the "tub" of your mister. What kind of mister is it?
I also use small black zip ties to affix things, the zip ties don't show up against the screen or vines but are secure which is nice. The ones that I got are just a little wider than the holes in the screen so you have to wedge it through and may move one of the "wires" that make up the screen to get it through.
Hope that helps!