Unfortunately, the Webpack HMR (i.e. the process that injects the updated stylesheets + scripts) only runs for the proxyUrl, which by default is localhost:3000 — or localhost:4000 in your case. This is only accessible on your host machine. It’s not ideal, but if you change the proxyUrl to your machine’s IP (with your chosen port number), it corrects the issue (i.e. 192.168.0.6:4000). (An alternate solution to Browsersync could be the Simulator app which comes with Xcode if you’re on macOS — assuming you want to test on iOS devices. localhost works on it.)
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