If this is the technology I think it is, it's a total scam.
In the 70's, a circuit came out of NASA to decrease the waste heat on grossly oversized motors. It found an application in the clothes industry, where the motors ran constantly, but the load was only occassional. Ta-da, the 30%+ myth was born.
The circuit kept being "reinvented" with microprocessors, etc. Of course the inventors would present this miricle technology to the appliance manufacturers (to managament, of course), and as a young engineer, I got my turn to test it and demonstrate that contrary to the invenor's opinion, it substantially degraded to performance of any near optimal design.
Funny enough, we kept a file on these attempts over the years. It had all the test results and consistent failures.
PS, what's in the box? Well, it's usually been a light dimmer circuit with some means to control the phase angle that it switches on.
There is no information on the product at that link! You can't even buy it there. So in truth it's impossible to comment on it one way or another.
However I recommend you read up on "Power factor correction" just in case that's how they claim it works. You also need to check how your electricity meter works because in many countries there is no cost penalty if appliances in your home have a poor factor. So improving the power factor won't save any money.
Power factor correction is only an issue for factories and offices that consume a lot of power and are fitted with meters that penalise you if you have a poor power factor.