They "work" because the most common form of evacuation for humans is urination. And that is easily cleared with a lower volume of water. The math is that even if you have to flush three times after you poop to get everything gone, you've saved water because most of the time you only peed and that took less water than it did before. The math checks out.
That said, washing is a different story. That is because washing is a chemical process, not a mechanical one. Regulation has simultaneously cut phosphates[1] (EDIT: per wikipedia the phosphates chelates the water which allows the detergent to be more effective) and reduced water (which is required for chemical action) and as a result the effectiveness of washing units (dishwashers and clothes washers) has in some cases stopped being effective.
Regulation itself has become less effective (in my opinion) because it continues to attack the symptom and not the problem. For example, it would have been just as effective to upgrade waste water treatment plants to remove all phosphates rather than ban them from detergents, however that solution creates a tax burden which can be resisted by a population whereas restricting the sale of products the consumer wants cannot be countered by the consumers directly.