Wages are only a small part of a products price, and there also is enough evidence that for example raising the minimum wage does actually help people.
For why it works, its simple: non-rich people spend any extra money, rich people don't do anything useful with their extra money. Which is also why trickle-down economics is a scam when its being presented as a way to help poor or average people. It does work of course as a way to transfer wealth from the poor to the rich.
Also, rich people don't do anything with their extra money? The exact opposite is true. Most of rich people's wealth is not in cash, it's in investments - while the average folk's extra money is "invested" in products that they can't afford, like the latest iPhone or a fancy house/car. No rich person that didn't just inherit their wealth lets their money sit in a bank except for a small percentage of their wealth, because they know it's a bad deal. How does trickle down economics transfer wealth from the poor to the rich? The poor should have wealth to begin with, in order for it to be transferred.