I had nothing to contribute to this thread because I make my own humidifiers but when I bought Glenn's Pineapple Sunday he kindly included not one but two Oasis humidifiers - so now I see how they're made.
As I see it, the ukulele version is basically designed to fall out of the strings! (I'm sure that wasn't the intent, but the way it is designed it is going to twist and fall out of the strings when the case and uke are turned upright and carried by the handle, etc.)
The problem is that as soon as the uke is turned upright (i.e. by lifting the case by its handle) the weight of the Oasis rotates the plastic piece that holds it to the strings. The "hooks" in the slots of this plastic piece are not sharp enough to prevent this happening because most of the weight is pulling the plastic into rotation instead of inwards toward the bottom of the uke.
If you put the humidifier in the sound hole as close to the neck as you can get it the tendency to twist and fall may be reduced - especially on smaller ukes where the body can't rotate far before hitting the inside of the "waist" of the uke. Placing it between the A and E strings might also help for the same reason - it will put the body close to the waist where it can't rotate as far. Finally, carefully cutting the slots in the plastic hanger so they actually reverse direction should help (though it will be a little trickier unclipping the Oasis to remove it).
EDIT: Actually, depending on the geometry of your uke it might make more sense in some cases to put the clip closer to the bridge end of the sound hole but turn the whole unit around so the body is pointing towards the neck. Basically, do whatever will put the body close to the waist so it can't rotate far.
HTH,
John