Alarm is working even when the phone is powered off I just discovered that if I set the alarm clock and then power off the phone (by holding the power button and then selecting "Power Off") the alarm will still go off when the time comes.

Is this expected behavior? It makes me feel like "power off" doesn't actually power off the phone.

I have a Huawei Y530-U051 running android 4.3.
That is expected behavior. It allows you to turn the phone off if you need to ensure the battery doesn't drain (or whatever other use-case you can think up) and still have a usable alarm clock. It's not new, many Android devices do something similar, and every iPhone since the first-generation models also had that feature. I can also recall an old Nokia 3310 I had back in the early 2000's which did the exact same thing.

Turning the phone off does shut down the OS, so don't worry about that. Android supports the setting of "hardware alarms", which let the phone boot automatically at a predetermined time. Not every manufacturer included support for them, but yours obviously did.

Edit: The hardware alarm feature has been deprecated by Apple and isn't useable any longer.