When referring to the allusion several hundred years old, what did the author imply about the immigrants in America?

Usually this is just called "repetition"!

But some more fancy terms for different types of repetition are:

Anaphora, which is repetition at the beginning of a clause or sentence.

Some less common cases are an epistrophe, which is repetition at the end of a sentence or clause, and a symploce, which combines both anaphora and epistrophe, meaning that it is repetition of the same phrase at the beginning AND the end of a sentence or clause.