It is compared to non-vaccinated regions, if you had bothered to read the article.

> To calculate mortality in the three countries, where death registry statistics are unreliable, the researchers employed tens of thousands of community reporters—more than 14,000 of them in Kenya alone—to conduct household surveys of childhood deaths in 79 areas where the RTS,S vaccine was administered and 79 comparator areas where it was not available.

That’s not how these kinds of trials work. The 13% figure comes from comparing the control and intervention groups, which were observed over the same period of time. The change in baseline mortality over time of the entire population isn’t relevant.

You really don’t if it’s controlled. The control group would have any other factors baked in.

If the group that got the vaccine has a 13% lower all cause mortality than the group that didn’t, and it was your standard randomized controlled double blind study, that’s a huge win.