I doubt bad jet fuel could cause a plane to explode*. More likely, it would cause the engines to fail. In that case, the crew would have time to radio that they were having problems. From the sketchy reports I've read, there was very little communication from the crews**. Even if the engines failed and took out the electrical generators, many airliners have backups like ram air turbines to provide emergency electrical power. It seems likely that whatever happened, happened quickly.

*According to some reports, eyewitnesses reported that one of the planes exploded. However, it seems eyewitnesses report explosions in nearly every airline accident when that usually isn't the case.

**Contrary to what many people believe, when an emergency happens, the first thing pilots are trained to do is to fly the plane, not reach for the radio. That said, the crew will try to communicate as soon as possible.