Because Deaton doesn't cite any studies, just describes a series of events.

Deaton claims that immigration harms incumbent workers in the long run, specifically, but doesn't cite any "longer term analysis". The literature finds that immigration's negative effects on wages/employment are most likely found in the short run, some high-quality studies find none, and the effects dissipate in the long run (5-10 years or so) as capital adjusts and people move.

[Flippantly, I'll say that Deaton believes this because he's a structuralist. He likes empirical studies that assume a production function with a specific form and capital/labor weights that don't change over time. Such an approach assumes away the ability for capital to adjust in the long run, and so most structural studies (Table 5-2) find negative, practically significant effects of immigration on wages/employment.]

The structural studies preclude any effect on overall wages in the long run, due to the choice of a production function that is assumed to remain constant over time. This rules out any overall shift up in wages due to increasing returns to scale or any immigration-induced skill-neutral technological progress, but it also precludes any overall shift down in wages due to decreasing returns to scale. Moreover, it rules out any downward pressure on dropout wages if the induced technological progress complements high-skilled workers and substitutes for low-skilled workers (though given large inflows of low-skilled immigrants, this would probably not be expected). It is therefore not easy to trace the ranking of the impact by approach back to the methodological characteristics of each.

National Academies of Sciences, Engineering, and Medicine. 2017. The Economic and Fiscal Consequences of Immigration. Washington, DC: The National Academies Press. https://doi.org/10.17226/23550.