I think its largely common sense that businesses would have sales to when money goes out. The same thing happens when refund checks come out. The author is of course biased, but that it not a reason to discredit the data. Are you suggesting he fudged the numbers for the graph?

If the oil dividend caused the decrease in inflation, you would be able to find many scholarly articles on the subject, yet the entire proof is a single graph.

No one is claiming the dividend caused it because causation is notoriously hard to prove since https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation. The author simply provides evidence in a graph that the after the dividend (Alaska's UBI) Alaska had a noticeably lower inflation rate compared to the rest of the US. Graph in question Take a look and make your own conclusions.