Exactly, I was the same. This is the News that Twitter was good for, the live events.
I’d always check Twitter for the initial on the scene explanation of what was happening from local people. In my case it was a massive warehouse fire that I could see the smoke in the distance. Obviously there was nothing about it on the traditional news sites, but loads of stuff from local people on Twitter immediately.
Then afterwards you’d just read the proper News outlets for the full official details after the fact.