Parse the statute a bit more carefully. The issue is not whether the crime has been brought within your immediate knowledge; it’s whether it was committed within your immediate knowledge, even if not in your actual presence. So if you are watching on security camera, say, while it is being committed, then it is committed within your immediate knowledge - i.e. you know directly (not through an intermediary) that the crime is being committed. If you only know about the commission of the crime because someone tells you about it then, no, it’s not within your immediate knowledge.
This doesn’t require presence or knowledge, but it does require that a felony has in fact been committed, and that the offender is in fact escaping or attempting to escape. Given those facts, if you have reasonable and probable grounds for suspecting that I am that offender, you may arrest me. But your arrest will be unlawful if, in fact, no felony has been committed, or the offender has not escaped or attempted to escape. Your reasonable and probable suspicion that both these things happened will not help you.
Remember, the common law loves liberty. Statutes which restrict your liberty (by giving other people the right to arrest you) will be strictly construed.