Is this behavior normal for lock screen and Phone app for android 4.1.2?
Depending on your ROM, there might be two settings for screen lock:


user turns of screen explicitly (default: lock immediately)
screen turns off by timeout (default: lock after 5 seconds if not switched on again by user before that)


You might wish to check with your device. It's usually found in Settings&rarr;Display. Not that this is not separately configurable on all devices.