If the phone is locked using PIN/Password/Pattern/Fingerprint and you say the "SafeWord", the device screen will light up to show you that the app has heard the"SafeWord" but you will need to unlock the phone to start the SOS.
To get around this, you can set the screen lock to "None" and when you say the"SafeWord" the SOS will start automatically. You can do this when entering an unsafe situation.