The post says they've taken a cursory look at emscripten to make sure it doesn't have "timing attacks" in one short sentence. This is exactly the kind of verification that requires an experienced and professional cryptanalyst to audit, examine, and finally confirm that emscripten -> js indeed doesn't expose the cryptographic algorithms to side channel attacks, or add additional weaknesses to the cryptography.

If the authors of the original post are not cryptographically confident enough to "roll their own crypto" how can they verify that their tool chain is secure?

Don't roll your own crypto, especially in using tools that haven't been verified to be used in crypto by cryptanalysis.