What did they do about rain?
If you are talking about Anatolia, I don't know. If you are talking about the Forestiere Underground Gardens in Fresno, CA, there is not much to worry about. Fresno receives less than 10 inches of rain per year. Mr. Forestiere designed his excavations so that the watter drained down to the lowest level -- 3 levels down. From their web page: "Forestiere built three underground levels; the first level is about 10 feet deep, the second is about 22 feet deep, and the third is around 23 feet deep. The lower levels also act as the main drainage point for most of the underground rooms and passageways." Apparently, he had no formal training in architecture and was self taught. He designed his gardens from memory of underground structures that he knew in Italy and learned his engineering from working on subways in Boston.
Rainwater was often the primary water source for ancient societies, particularly in desert areas and islands, where wells were scarce or brackish. The Nabatean city of Petra in modern Jordan captured square miles of runoff (with no vegetation, the rain flash-flooded, just as it does in many places in the western US), storing it in cool, underground cisterns dug out of the bedrock, and controlled a lot of trade that way.