fmstyle runs entirely locally (CLI) or entirely client-side (web app) and makes no network requests. Still, if you believe you've found a security issue — e.g. in how the web page handles pasted input, or anything that could cause the formatter to alter what a calculation computes — please report it privately:
Please do not open a public issue for security reports. You'll get a response within a few days; fixes ship as a patch release with credit if you want it.