Well, first, you shouldn't actually have the net pots in the solution like you do. You want the net pots to be almost touching the solution but not quite. The bubbling action of the air stone should wet the bottom of the net pots.

What keeps my air stones in place is that I drill a hole in the lid of the DWC that is the exact same size as the tube and then feed it through. Since it fits so snugly this keeps it in the location I want. One reason the airstone may flip over is that the tubing is kindof curled in the wrong direction to keep the stone upright. You can try twisting the airstone while attached to the tube and see if you can get the right setup that way.

Your clear box will grow algae. It's better if it's either painted black or covered with foil so that light does not hit your nutrient solution.

What cole said is very important.
What Ethno said is also accurate. To add to his comment, I would also suggest you can attach it to the bottom of the tub with some silicon. Just let it cure before adding water. Also, as Ethno said the bend in the air line tends to lift it up. try to fix that so it doesn't pry the stone off the silicon. ( a little pry over a long time will eventually get the job done)

I use suction cup with a zip tie through it and around the hose; as it is fixed into the back of air stone. You can also add another zip tie around the air supply line just behind other; to prevent first from sliding down the barb of the air stone and falling off.

simple fix is silicone. hands down set it and forget it. there is going to be more issues as time goes on to have to worry about your air-stone issue not trying to be rude but its true. i have a very similar system and i just add some silicone and your all set bud.