I believe the water shortages are due to the unlicensed drilling of wells, to provide water for the abundance of qat bushes, which seem to be a big part of the Yemen economy. There is a desalination plant at the refinery. The water (steam) is used to run the power station.
I was recently referred to another article by the Carnegie Institute which paints a better economical picture for Yemen. The article can be read at this link.
We lived in Aden from 1969 onwards till 1972. We never faced any water issues at all. It was always there straight from the tap and in the fridge in emptied orange squash bottles for cooling.
There was something about Aden water though, I always felt hungry and my mom often got tired of cooking all the time.