Must depend on location. ABC 33/40 said Tuscaloosa sirens were down also from previous outbreaks Birmingham videos have the sirens sounding continuously, but in today's videos there are no sirens playing off in from each photographers vantage point. With a tornado that large hitting as many connectors, transformers and power lines many siren systems were probably knocked out miles in advance of the tornado. Also, coupled with all the storms and power outages from this mornings storms... sirens may have failed many today.
Also, not just sirens but probably the EAS or even ability to reach local media warnings too with loss of power. Also noticing a lot of videos on Youtube the authors didn't even know they were looking at a tornado with the massive wedge because it was so big.