  We analyze the explosion problem for a class of stochastic models introduced
in Part I (arXiv:2103.06912), referred to as doubly stochastic Yule cascades.
These models arise naturally in the construction of solutions to evolutionary
PDEs as well as in purely probabilistic first passage percolation phenomena
having a Markov-type statistical dependence, new for this context. Using
cut-set arguments and a greedy algorithm, we respectively establish criteria
for non-explosion and explosion without requiring the time-reversibility of the
underlying branching Markov chain (a condition required in Part I). Notable
applications include the explosion of the self-similar cascade of the
Navier-Stokes equations in dimension $d=3$ and non-explosion in dimensions
$d\ge 12$.
