It's important to understand the limitations of the paper. the paper simply plotted a set of regions where the outbreak happened, and analyzed the growth rate in these regions vs the average climate in that region. Notably, it did not include areas where there was no growth (which coincidentally, are almost universally hot or tropical regions). If those were included, you'd have seen a much larger effect.

With that said, even with just including areas with the epidemic - it found a statistically significant effect. Just, as you note - not a significant effect (which doesn't mean that a significant effect might not exist)