Many states limit citizen’s arrest powers such that if the crime at issue was only a misdemeanor, the citizen can only arrest if the citizen actually saw it happen. In the OP’s question, it seems clear that the citizen did not see the original crime. As others have noted, flight from the police can itself be a crime, but I would be leery of trying to make an untutored decision as to whether someone is committing misdemeanor vs. felony flight.
Moreover, as a gross generalization, a police officer arresting someone has a defense of qualified immunity against mistake of fact. In other words, if the police officer is acting based on probable cause, she can forcibly detain someone and not face liability even if that suspect turns out to be the wrong person. If I – an intrepid but ordinary citizen – decide to help the police by forcibly detaining someone, I might be able to establish a defense of justification if it turns out to be the right suspect, but if it’s the wrong person, I’m not sure that I would have any defense against civil liability (and criminal charges).
And then, of course, my use of force has to be reasonable under the circumstances.