Hi,
I could not see anything more serious on the concern that you been raised.
so from the scenario what i assume is, you might had claimed the point of work experience, and to support the application, as a evidence you might had sent the IRD summaies of earning (which will though clearly show the companys name and that he wages and taxes are paid appriopriately.) BUT thats not the only thing he is asking for.
He is looking for a letter from your ex employers (that you claimed for) letter, where they clearly mention
the exact dates you were employed, the position you held, the hours per week you were employed for and a brief summary of your duties in this role. (job description) so He is just after a confirmation letter from your ex employer. I guess thats all. goodluck