Wecharacterize disjoint hypercyclic and supercyclic tuples of unilateral Rolewicz-type operators on $c_0(N)$ and $ell^p(N)$, $p in [1, infty)$, which are a generalization of the unilateral backward shift operator. We show that disjoint hypercyclicity and disjoint supercyclicity are equivalent among a subfamily of these operators and disjoint hypercyclic unilateral Rolewicz-type operators always satisfy the Disjoint Hypercyclicity Criterion. We also characterize simultaneous hypercyclic unilateral Rolewicz-type operators on $c_0(N)$ and $ell^p(N)$, $p in [1, infty)$.