Are you starting the song by hitting Play on the device running ST3? or a foot switch? or MIDI trigger?
My drummer uses a Roland SPD-SX PRO to trigger song start and we always see around a 1/4 to 1/2 beat delay in song start as compared to when I hit the Play button on the iPad.
Also, is the song definitely not playing for those few seconds? Or is the song playing (play head on the waveform bar moving, countdown timer moving), but you are not hearing any audio output?