if f is symmetric monoidal then so is the map Psh(C)-->Psh(D), where we take presheaves of complexes. so f_!(a \otimes b)= f_! a \otimes f_!b. In terms of Tor stuff, maybe it's better to write as `$Lf_!(a\otimes^{\mathbb{L}} b) = R=Lf_!(a) \otimes^{\mathbb{L}} Lf_!(b)$. So you can compute that with a composite functor sseq, right?