I think J.S. Mill was the first to use the black swan as an example in the problem of induction. Popper was just channelling Mill. I’m not sure what inspirted Taleb to use the phrase. As someone who teaches philosophy, it’s really annoying that the classic example has been hijacked by something that refers to something quite different. It’s also a strange choice as Taleb’s black swans are supposed to be rare, whereas the whole point of Millean black swans (and black swans in the world) is that there are literally thousands of them!
I’m a huge fan of Popper. I don’t think he solved the problem of induction (as he claims — he just moved it on down the line a little) and I think falsification is problematic, both theoretically and practically (qua Duhem and Quine), but most of what I teach and, I hope, most of what I practice is Popperian in essence.