Yea, it's the combo of the chiller and cooling tower is analogous to a swamp cooler. The cooling tower provides the evaporative cooling. The difference is that rather than directly cooling the environment around the cooling tower, the chiller allows indirect cooling of the DC via heat exchange. And isolated chiller providing heat exchange is why humidity inside the DC isn't impacted by the evaporative cooling. And sure, humidity is different between hot and cold isles. That is just a function of temperature and relative humidity. But, no moisture is exchanged into the DC to cool the DC.

Edit: Turns out I'm a bit misinformed. Apparently in dry environments that can deal with the added moisture, DCs are built that indeed use simple direct evaporative cooling.