[kr0bat]

The paper was very careful to describe the mass increase of Cuban immigrants as "immigration shock", not just immigration. I don't think the conclusions of this paper can say any one thing about the effects of our (I'm assuming you're American as well) standard levels of immigration. Also..

  These results suggest that immigration shocks do have implications for the fertility decisions and outcomes of natives, though these tend only to be temporary and short-lived. There therefore appear to be little long-term or sustained consequences for the fertility of natives from governments pursuing labour augmenting strategies through more open immigration policies.

From the conclusion. I only really skimmed the abstract and the conclusion, please tell me if I'm missing something.

[jevoten]

> standard levels of immigration

Immigration to the US is at its highest level since the 1910s, in both absolute and relative terms: https://cis.org/Graph-Immigrants-US-Number-Percent