1. As a non resident alien, you are subject to US tax on business income if you are “engaged in a trade or business in the United States“, short “ETBUS”.
2. You are ETBUS only if two things are true: (i) You have at least one “dependent agent” in the US. Dependent agents are employees or companies that work almost exclusively for you. And (ii) that dependent agent does something substantial to further your business in the US. Purely administrative jobs are not included under this rule.
3. Finally, if you can benefit from an applicable tax treaty, then you’re only subject to US tax if (in addition to being ETBUS) you operate in the US through a “permanent establishment” (e.g. an office or other fixed place of business). If you don’t meet those conditions, you are not (automatically) subject to US tax on your business.
Even if the LLC generates income in the US, by offering services or selling products into the US, that income is not taxed in the US.