Your description is kind of hazy. So when you have been using the DMs, you turn the screen off like you're putting it to sleep and then it will still open when you press the power button like it was never locked? Or am I describing this incorrectly? What device do you have?
If my description is accurate what could be happening is you are not reaching the lock timeout. There is a screen on timeout and a lock timeout. obviously the screen on timeout, times out after inactivity and puts the screen to sleep and locks the phone. The lock timeout begins when you hit the power button to put the phone to sleep. So you hit the power button the screen turns off but if your timeout is set to 30 seconds or 1 minute if you turn the screen on within that time it will act as if you never left. The lock timeout can be set to "immediate", in which case every time the screen is put to sleep, even if for just a second, the screen locks.
Not sure where you would find this on your device since we don't know what device you have but it could be under security, for the device lock, or it may be under display, for what to do when the screen is turned off.
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