If the matter is strictly summary, the DPP will not become involved. The Police appear as prosecutors in summary matters. Additionally, summary offences do not have committal hearings, only indictable offences do.
If you wish to enter a plea of not guilty, brief orders will be made. Usually, the Prosecution will have 4 weeks to provide you with the brief of evidence and there will be a "reply" mention date 2 weeks after the Police have served the brief upon you or your lawyer. The reply date allows you to either, having read the brief of evidence, enter a plea of guilty, or alternatively, confirm your plea of not guilty and set the matter down for a defended hearing. On the date of the defended hearing, the Police will bring their witnesses and you or your lawyer will have the opportunity to cross-examine them. You will also have the opportunity to give evidence and call witnesses that will assist you.
It is correct you should not agree to the facts if they are not an accurate representation of the truth. You are sentenced by a Magistrate on the facts that are tendered, so if you do plead guilty, it is important that they are an accurate reflection of what occurred.