What is importance of author listings when resumé/CV differs from actual publication?
In general, author position must be the same on a CV as it is in the official publication. Changing author position on the CV is generally deceptive. In particular, first authorship often conveys a greater role on a publication. So this may suggest the applicant is trying to indicate that they had a greater role in the publication than they did.

That said, it seems like a rather strange thing for an applicant to do. If someone is going for an academic job, it is common that the employer would have a look at a few publications. Thus, it would quickly become evident that CV and publication differ in author-order. And this would typically be perceived poorly by the employer.

A common and better strategy is to bold or star your own name in the CV (and perhaps the names of students you have supervised). This makes it easier for a reader of a CV to scan author position.