Ever heard of clickbait?
It is unlikely Tehran will just evacuate all at once. They will do something drastic when the problem can no longer be ignored. And random events like rain will delay the inevitable for a while longer.
Perhaps this is how climate change will end up as well.
It IS climate change, to a large part. And yes, I think you're right it's how climate change will show up for us as well.
There will always be lot of other factors - the first time we're going to really collectively notice sea level rise is on the high tide during a storm surge. The rest of the time, the change will be within the range of variation that we're used to dealing with.
Ever hear of reading the article you comment on? There was no mention of "moving all at once". As stated, moving the capital from Tehran "would take decades"...