The book is correct in reporting that the corresponding DNA sequence for the AUG site on the mRNA would be ATG (not TAC).

The mRNA is made from the template strand of the two strands of DNA; that is, the double stranded DNA denatures--the two strands separate --and the RNA polymerase II only uses the template strand. However, when one reports the DNA base sequence that corresponds to a sequence of RNA, convention is that the template strand is not reported; instead one reports the "coding" strand. See figure below (from Becker’s World of the Cell). So an A on the mRNA would correspond to a T on the template strand (A pairs with T, G with C), but the coding strand would be reported: another A. The coding strand and the mRNA would be the same sequence except that the coding strand would have a T instead of a U (DNA has ATGC, whereas RNA has AUGC).