The alarm working when the phone is off is a normal (at least for every phone I've had so far) and also desirable (in my opinion) thing. If the battery is too low for the phone to be able to receive touch screen input, it might be annoying in rare cases (like yours), but still this "feature" is a good thing. The alternative would be that the alarm doesn't work when the phone is off, which is definitely not good.
A possibility would be for the alarm not to work when the battery is too low. I'm not sure though how useful that is. Even if it might be slightly annoying I'd prefer my phone to wake me up even when it's almost out of battery, even if I can't turn the alarm off.