How does a drastic change to the genome persist and spread?
It isn't necessarily true that individuals with different numbers of chromosomes are infertile. Even though common wisdom has it that horse (64 chromosomes)/donkey (62 chromosomes) hybrids are invariably infertile mules, that's not true; a significant number of fertile horse/donkey offspring have been documented.  Here is an example where the chromosomes were checked and confirmed to be 63 in the fertile mule parent. 

Even more dramatically, the common shrew (a single species) has many different chromosome numbers as natural variability (at least 50 different chromosomal variants were identified in one paper) and this doesn't affect their interfertility.

So there are three general answers to the question here, though I don't know which is the most likely.


The extra chromosome arose and the original variant was very fortunate to have offspring; similar to the rare horse/donkey fertile hybrids.
The extra chromosome arose but had little effect on interfertility; similar to the common shrew. (The quote from the article in the question argues against this, but I don't know if it's a presumption made by the researchers, a presumption made by the writer, or a demonstrated fact.)
The extra chromosome arose in a single litter, so that several siblings shared it, and then interbred. Although incest avoidance is generally quite strong, animals that colonize islands or distance geographic areas (invasive species, often) commonly do interbreed this way.