I can't see the paper, but there is some interesting technical details in the supplementary data https://static-content.springer.com/esm/art%3A10.1038%2Fs418...

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.