In our article in MCU'13 we state the the Domino problem is undecidable for all Baumslag-Solitar groups BS(m, n), and claim that the proof is a direct adaptation of the construction of a weakly aperiodic subshift of finite type for BS(m, n) given in the paper. In this addendum, we clarify this point and give a detailed proof of the undecidability result. We assume the reader is already familiar with the article MCU'13.