I think the article addresses this fairly well. In addition to shade, evaporation from open water and plant leaves contributes, as does the soil acting as a heat sink.

Botanical gardens are only slightly more effective than trees over roadways from their study, so shade is likely the strongest factor, but the others clearly play a part- from cooling down enough overnight compared to roadways and cement to the evaporation from the denser vegetation having a stronger effect.

The thing that I missed was how such a garden compared to an open, grass park. The difference in vegetation density would be clearer, I think, and might better explain the difference measured between trees over roads and gardens.