There's another solution for that... Weather Channel has free email alerts you can set up to be delivered for warnings - and if you get them sent to an email account you have set up for push to your iPhone, you will get them quite fast - and will be as fast, or faster than local TV stations run automated crawls with alerts.
And still another solution: subscribe to weathertap.com - awesome radar on a home computer, or - on a mobile device - phone, or tablet... plus, they offer an email or sms notification service that's included with your subscription that sends weather warnings - and those are delivered as fast or faster than broadcast media delivers as well.
Edit to add: I have reviewed the available apps in the AppStore that purport to be what you are looking for, and none are rated well at all - and those that I've tried live up to their dismal ratings. Your best bet is either of the two methods above, or both for good measure.