The way you phrased your question actually allows for one solution which is simultaneously "science-based" and yet "almost like a psionic ability". But to earn the evolution tag, we must stretch its definition to include the products "developed by" naturally evolved intelligence, such as technology...
We need to start with the Emotion API which is part of the Azure Cognitive Services. This is a software service product, which when fed a still image or video stream, will interpret the emotional state of any human faces which it "sees".
Now take this product and let it mature at the speed of technology and it will undoubtedly become staggeringly accurate; interpreting barely visible micro-muscular facial motions with instantaneous speed and near perfect accuracy.
Once the service is ready, all we need to do is integrate it into the next generation computer interface which Samsung and others are working on, contact lenses.
If such a product became commercially available, they would quickly saturate all markets; probably even faster than cell phones did. Anyone wearing them would have such an advantage over everyone else that soon everyone would have to have them.
It isn't really evolution, but I would not be surprised if it's a genuine prophecy. I can't wait to buy mine.