I'm a native English speaker, and that term is definitely wrong for a wake-up alarm. I can't imagine an alarm for when to go to bed, and it definitely doesn't apply to what someone would set on an standard "alarm clock" to wake them up in the morning.

Even when it's a phone call instead of an alarm we say "wake up call". I've never, ever heard the phrase "bedtime alarm" before.

I really hope Apple didn't call it that.