In most course books for German (esp. DaF) is written that you have to use a perfect tense form a step back from what follows, e.g.
Wir reden weiter, nachdem wir gegessen haben. (Präsens - Präsens Perfekt resp.)
or, as both events in the sequence usually tend to have occured in the past,
Wir redeten weiter, nachdem wir gegessen hatten. (Präteritum - Plusquamperfekt resp., the classical example from the course book)
depending on the temporary position of the main clause (here: wir reden weiter/wir redeten weiter), the first corresponding Present Continous in English grammar and referring either to present or future situation
However, modern German goes somewhat beyond and combinations of Present Perfekt and Präteritum are typical for a sequence of events in the past, as one tends not to use Past Perfect (Plusquamperfect) in der Umgangssprache at all:
Nachdem wir unsere Zimmer bezogen haben, machten wir uns auf den Weg, um einen Strandspaziergang zu machen.
Colloquial German often simply ignores the prespription of the course books to use different tenses for a sequence of events with nachdem and uses perfect for both, e.g.
Nachdem wir uns beschwert haben , haben sie wenigstens gestaubsaugt
It is also possible to put both in Präteritum, it would sound somewhat South German or seem to be an attempt at literary writing, e.g. an essay "how I spent my summer".
Nachdem wir aufwachten, machten wir uns an die köstliche Morgenmahlzeit
As for the book having a mistake or not, it all comes down to the purpose of the book and the limitations of its size/its target audience. If this is a book preparing your for a language test at your school somewhere abroad, or probably even some international language test, this is not a mistake but trying to teach you pass the exam using "correct" "book" German. If this was an elaborate 2000 paged grammar of contemporary German, I would find this to be a mistake.