I wouldn’t be surprised if the wisp of steam you saw was transmission fluid cooking off, but that doesn’t mean you should ignore what VDC said. It’s certainly possible you have a cooling system failure, as well as a failure of the engine temperature sensor that’s supposed to tell the gauge when it’s too hot.
I have difficulty believing that the alternator was the cause of your loss of power. If the RPM’s went way up, the power went down, and the transmission fluid was burned, then you may well have a cooked clutch. In fact if the previous mechanic was incompetent enough it’s possible that he stupidly somehow got transmission fluid into the clutch, and now it’s lubricating the clutch friction plate (which is not supposed to be lubricated) which is causing it to slip, which is heating it up. If that’s the case, you’re in for a new clutch.
If the alternator died, your car would continue operating as normal because the battery would power the car. If the alternator died, and you ran the car long enough to drain the battery, then you wouldn’t have been able to restart it to turn the AC on.
The new mechanic’s explanation for what made the car do what it did simply doesn’t make sense. I’d make sure that what you wrote here is really what he meant to tell you, and if it is, find another mechanic.