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I figured this out by going to the author's publicly available github code. It turned out the authors were just generating the transition probability $p$ from $\mathcal{N}(\mu,\sigma^2)$ at the beginning of each episode for some reason. Answering it myself for the sake of not leaving this question unanswered.


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The conventions I have seen tend to post-multiply rather than pre-multiply, although there are examples in the literature which adopt the opposite convention. Some examples include: In Deep Learning: An Introduction for Applied Mathematicians, a layer with input $x \in \mathbb R^n$ and output $f(x) \in \mathbb R^m$ is computed by $$ f(x) = \sigma(Wx + b)$$ ...


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