I'm not sure whether it was by design or by accident. To be able to answer that with a high level of certainty, we need to ask the people who designed the incentive payment.
Looking at the numbers, I would say it's due to different consumption patterns. Poorer households have less money to spend, while richer households tend to have more people and spend more. They drive bigger cars, drive longer distances, have bigger houses that need more fuel for heating purposes, consume more electricity when the electricity is generated using carbon-intensive sources, and so on. Because of the different consumption patterns, richer households tend to have a bigger carbon footprint, so to speak.