I read the following exercise in the book of Rotman: "an introduction to homological algebra"

9.21: In the situation $(_RA, _SB_R, _SC)$ with $B$ $R$-projective, use the adjoint isomorphism to obtain isomorphisms $$\mathrm{Ext}^n_S(B \otimes_RA, C) \cong \mathrm{Ext}^n_R(A, \mathrm{Hom}_S(B, C)).$$

I consider the following example: $S = \mathbb{Z}, R = \mathbb{Z}/2\mathbb{Z}, A = B = C = R$. Then $$\mathrm{Ext}^1_S(B \otimes_RA, C) \cong \mathrm{Ext}^1_{\mathbb{Z}}(\mathbb{Z}/2\mathbb{Z}, \mathbb{Z}/2\mathbb{Z}) \cong \mathbb{Z}/2\mathbb{Z}.$$ And $$\mathrm{Ext}^1_R(A, \mathrm{Hom}_S(B, C)) \cong \mathrm{Ext}^1_{\mathbb{Z}/2\mathbb{Z}}(\mathbb{Z}/2\mathbb{Z}, \mathbb{Z}/2\mathbb{Z}) \cong 0.$$

So what is the incorrect: the exercise or my example?