How to use atom-typescript or alternative with eslint
I had the same problem and the issue on linter-eslint GitHub's repo helped me.
You need to tell linter-eslint that it actually knows how to handleTypeScript files.
You can do that by adding the scope for TypeScript files (source.ts)here:
The screenshot above is from settings page of the package linter-eslint (Preferences > Packages > linter-eslint).
I've added source.ts and source.tsx, reloaded the window (View > Developer > Reload window) and Atom started to display my lint errors.