By what magick do temporary workers depress wages but immigrants not?
They don't. If someone's paid cash under the counter, it means that the business is getting the labour for less than they'd need to pay to get a legal worker. That means that the demand for legal workers at a proper wage is reduced, so those going for those jobs are going to need to accept less money as a result of the competition for fewer positions.
That's why minimum wage laws are important and why there should be severe consequences for businesses which hire illegally. I am against Trump's policies, but that's because he's going after the wrong people. It's the businesses which should be targeted and which should be the focus of ICE activities, rather than the immigrants. Clamping down on businesses will have the effect of reducing the attractiveness of the country to illegals and reduce their numbers as a result, but won't be quite so dickish about doing so.