If it doesn’t what does it do?
I also say “your phone is going off” as it can refer to either the alarm, incoming call, or other notifications. It’s definitely an accepted alternative meaning for the phrase.
“Going off” can also mean “be in the process of spoiling / going bad” when referring to foodstuffs, which I only mention to point out that the phrase has at least one alternative use beyond exploding, even if alarms and such aren’t considered. More usually in the past tense of “gone off”, but it gets some use in the present tense.