I have a Galaxy S3 phone and a Galaxy Tab 4, both with the same issue. I'm using the Echo Lockscreen app (paid version) with a pattern unlock, which I'm happy with. I'm also using the built-in "Clock" on the phone and "Alarm" on the tab.
When the alarm rings and I shut it off, the phone/tab is unlocked - so it skips the unlock security. Using the stock Samsung lock screen, the lock works and I have to unlock the phone normally.
I'm not finding any settings either on the device or in the app - any ideas on how to fix this? I'd be willing to switch to a different alarm clock app, but I'd like to keep the lock screen unless there's something as good as this one.
I can switch Echo to use my system unlock method instead of its own, but the user experience is kind of crappy there - you have to unlock then also swipe away Echo.
If someone steals/finds my phone, I'd rather not have it unlock automatically for them if I don't remote-wipe it before 6am the next day.
EDIT I'll be getting a Galaxy S6 in a few days to replace the S3, but I'd guess it will have the same issue there as well - but I don't know for sure.