First of all, you need to notice that the glass used for screen protectors and as a screen cover glass is far more advanced than what you find at your local bus-stop. Gorilla Glass and the likes are Alkali-Aluminosilicate glasses that get chemically tensioned by exchanging the smaller natrium for potassium ions in a molten salt bath.
Since the compressed surface layer created by chemical tensioning is very thin, the glass still shatters in big shards, which is actually advantageous for the application. If you want safety-glass that shatters into thousands of dull pieces, which is probably the kind of tempered glass you had in mind, you put regular soda-lime-glass though a classical thermal tempering process.