Is my textbook wrong about phonetic transcription?

I would say that the textbook is correct: that barring squabbles over the substance of the phonemic analysis, the book has provided a phonemic transcription, and not a phonetic one. For example, there would be "ʰ" all over the place to indicate the phonetic aspiration that exists in English. In notates "jingle" with a cluster /ŋgl/, lacking the syllabic diacritic under l which would be in a phonetic transcription. This being UK English, I don't know what other phonetic details are missing. It does make some choices about phonemicization, writing /əʊ, i:/ which could equally be /o: o; i/, but that is consistent with the range of possible analyses of English.