TLDRV They divert the rainy season water to natural aquifers and hope it reappears down river in the dry season. The small scale of the effort currently makes me a little skeptical that it's achieving anything. Underground water is impossible to measure. What might be more effective and certainly more measurable would be to build a dam/reservoir.
The linked paper > Infiltrated water is retained for an average of 45 d before resurfacing, confirming the system’s ability to contribute to dry-season flows. We estimate that upscaling the system to the source-water areas of the city of Lima can potentially delay 99 × 106 m3 yr−1 of streamflow and increase dry-season flows by 7.5% on average, which may provide a critical complement to conventional engineering soluti…
In page 15, table 2 they show that they put some Eosin https://en.wikipedia.org/wiki/Eosin upstream before the water entered the earth, and then they collected water from the springs downstream a few weeks later and measure how much Eosin was there, and used this to estimate how long the water was stored.