I'm in the county, not the city. During a rainstorm, I doubt that I'd hear our city warning siren if I was sleeping. Thankfully, I'm scared to death of tornadoes. Been through several close calls. So, I have a scanner that screeches if there is a warning....otherwise, if it's storming, I just don't sleep!
That scanner is the very best way to go,,,bar none,,,
I do like the warning for the public though,,,
Like you, if I hear that we MIGHT get tornados at night...I don't sleep, I don't trust any alarm going off.