I personally tried to use SublimeLinter with SublimeLinter-contrib-tslint, but it did not go over to errors - it kept saying that there were no lint errors, although I could see them on the screen in separate files.
The closest I could get is what Atom provides (that I decided to step back due to lagging scroll navigation):
1) Selection, for example: Tools> Build system> TypeScript
2) Show console (Ctrl +)
3) Tools> Build (Ctrl + B)

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