For a real DDoS being woken up at night won't make a lick of difference (either your ADS/pipe can handle it, or it cannot). As such, waking up for it makes no sense at all. For this, you should blame your employer.
The guy who woke me didn't know it was a DDOS, all he knew was our service was down. It doesn't matter whether I can do anything about it or not, someone still gets phoned when this happens.
The whole point of addressing alert fatigue is preventing such misunderstandings from happening. I understand that it could have been a mistake, in which case the thing to address would be to not wake anyone up in this scenario next time.