I've put the word "evacuation" in the title of this piece in quotes because it's not clear where Tehran's 9.8 million people or some significant number of them would evacuate to as water supplies run dangerously low. Iranian President Massoud Pezeshkian has been criticized for saying out loud how bad the situation is: "If it does not rain in Tehran by December, we should ration water; if it still does not rain, we must empty Tehran."
Doubtless Iranian water authorities will force severe restrictions on Tehran's residents if the rains—which have been 82 percent below the long term averages for the past year—do not come. And there is almost certainly room to conserve. But the relentless heat (and thus increased evaporation from reservoirs) and lack of rain are not something that can be put down to water system mismanagement unless (as you should) you count not understanding and reacting to climate change as a failure of management.
Back in 2018 Cape Town, South Africa was facing a severe water shortage for lack of rain during which the city began making announcements of a specific date which it called "Zero Day" when water would have to be shut off to most of the city. Dramatic conservation which drove water consumption down 30 percent and the return of seasonal rains saved the city (for now).