How do the citizens of Arcanretia know that Aqua purified their hot springs?
Actually, hot spring water usually does show a subtle, if not significant, difference in color as compared to normal hot water.

Referring back to my previous answer of how in Arcanretia, hot spring water vs normal hot water is analogous to onsen vs sentō, if you were to look at stock photos of onsen baths, you could see that the water is somewhat cloudy and unclear:


(source: hikyou.jp)  

You can probably tell the difference between that kind of water and clear, normal hot water.