if A is decidable then B is decidable too
By definition, a language $L$ is decidable if there exists a TM $M\mid L = L(M)$ deciding it. Consider a TM that rejects on all inputs (for example, one where $q_o = q_{\text{rej}}$). The language of this TM is $\emptyset$, so $L=\emptyset$ is decidable.
With reductions, in general if $A\leq B$ ($A$ reduces to $B$), then $B$ is at least as hard as $A$ with respect to decidability. An undecidable language $A_{TM}$, regardless of what it actually is, is harder to decide than the decidable language $\emptyset$ by definition. The specifics of the reduction don't matter; the only information we needed was given in the problem statement (that $A$ is reducible to $B$).