I've never used that product but I believe the addition of caffeine is supposed to promote the firming/tightening of skin when an ingredient in creams - they use it in anti-cellulite creams etc. but I don't think there has been any conclusive proof as to whether this actually works.
Then again, it's also a diuretic but I seriously doubt that topical application could depuff swollen undereyes. Perhaps I'm just naturally sceptical. :|