What is continuous selection?
Continuous selection is not a term; it would not be bolded in a textbook.

When studying the history of a genome/lineage, you could have two very broad hypotheses about a given trait:

1) The trait was not present in a lineage, then appeared fairly suddenly (at least on a long time scale, it could still be hundreds, thousands, or millions of generations), and since then did not change much.

2) The trait was not present in a lineage, then the trait appeared in part of that lineage, and since then, the trait has continued to change substantially among different descendants of that lineage.

You could find evidence towards (1) if, for example, you observe a trait that is fairly constant among a diverse modern taxon but you don't see a similar trait in the cousins of that taxon.

You could find evidence towards (2) if you see a lot of diversity even among recently speciated members of a taxon.

The statement in the article is just saying in plain English, rather than using a scientific terminology, that they see evidence towards (2).