Good point. It does seem like the ryshadium have spread out into the rest as Roshar, and Shin plants mostly stay in Shinovar, which has a very different climate to the rest of Roshar. Aside from evolution, it seems unlikely to me that the Shin would learn rhythms, considering how xenophobic they are.
Although I just realized that maybe they are just getting in tune with the rhythms of Roshar, and didn't learn from the listeners. The shin consider the stormlight to be holy, and it doesn't seem unrealistic for them to feel the rhythms in stormloght or lifelight and try them out.