That would be really interesting though. A child named Tim unwittingly time travels to save his life, but there are consequences when time iself starts stalking him in an attempt to “correct” the alteration of the timestream’s intended “flow”. No matter how it tries, it can’t physically harm the child (that’s generally not how time works), but makes up for it by attacking his mind. Many years later, a man named Alex Kralie time travels to save his friends’ lives.
Cheated twice, time finds the perfect way to fix everything. Seeing as Alex has manipulated time (much more than Tim had), time manipulates Alex into “fixing” what he did. People who had nothing to do with this also get dragged into it because this wasn’t what was supposed to happen. Their involvement is a direct result of the timestream being altered; thus the consequences affect them too.