This device was developed by Cinthia Rowland, an esthetician that promotes facial exercises to fight wrinkles, she even has a book about it. Regarding facial exercises results, this device is just a vacuum adapted to lips shape, seems it works just causing inflammation due to suction (more blood flow to the lips), thats why the effect only lasts for few ours after each use and, according to the reviews, if you over use it may get bruises. 

Most lip plumpers formulas have an irritant like peppermint oil and
cause irritation, the lips gets a little swollen. This device just seems
to cause inflammation in more "extreme" way.

What concerns me is the long term effect of the inflammation - back to normal cycle, the everyday suction may cause the breakage of collagen and elastin fibers resulting in wrinkles and saggy skin.