Like just about every modern handgun out there, there is a firing pin block/safety in the slide that prevents the firing pin from moving forward unless the trigger is pulled. Other popular striker-fired guns that use a similar pre-cocked striker system are the Springfield XD, S&W M&P, SIG P320, Walther PPQ, and the new Walther PDP.
The trigger safety is only there to help prevent the trigger from moving completely to the rear (thus disengaging the firing pin block and discharging the pistol) should anything but a direct trigger press occur.