Is finding all cycles in a graph using some version of Johnson's algorithm (code provided) really polynomial (benchmark provided)?
The question seems based on a faulty premise. There are multiple algorithms that Johnson invented, and you're confusing them.  One of his algorithms is for finding shortest paths (that's the one Wikipedia article talks about), another is for enumerating all cycles (that's the one the Stack Overflow answer cites).  They don't have the same running time.

Second, you're using some random person's code, but maybe that code sucks and isn't a good/valid implementation of the algorithm.  We don't do questions about code here.

Also, as David Richerby says, you obviously can't output all cycles in polynomial time if there are exponentially many of them (where there can be).  Therefore, you shouldn't expect an algorithm to enumerate all cycles with polynomial running time.

Finally, you can't disprove an asymptotic running time analysis by benchmarking it on 6 points.

I think you need to read Johnson's original paper, understand it, and implement it yourself.  Sometimes there are no shortcuts.