In fact, most mid and higher incomes remain relatively static in response to a minimum wage increases at the low end. This means that minimum wage increases get passed into the business owner and customer who do not usually agree to a higher price for the product.
This, what is more likely to happen is that people decide that they can only preserve their income by replacing the minimum wage workers with automation, or they just get out of the business altogether.
In other words, minimum wage increases ultimately price the low wage worker entirely out of employment.