Physics professor says that if event A caused event B, some observers could still see event B happening first. Is this true?

The example he gave was that Gordon Hayward got injured. As a result, he cried. The question is, would all observers see this? Or would some see him crying before the injury?

I understand in relativity two "simultaneous" events don't necessarily happen at the same time for all observers. In this case however, doesn't the information of the injury need to travel (at most, the speed of light) to my professor, causing him to cry?

In this case, its impossible for any observer to see him cry before the injury, correct? Is there a thought experiment to help myself understand this?