Discovery obligations in California are dictated by Penal Code section 1054 et. seq. The short answer to your question is that the prosecution is bound by not only state statutory law, but as you said, Brady. Under statutory law, the prosecution must turn over witness statements, identity of witnesses, and the like, within 30 days of trial. That applies to the witnesses the prosecution intends to call at trial. That does not include rebuttal witnesses. The argument is that they don't know what witnesses or statements they will use in rebuttal until the defense puts on its case.
You should look at California Penal Code section 1054 ET seq. These are the discovery statutes. The DA is obligated to provide a witness list 30 days before trial. If a witness is obviously known, such as a witness listed in a police report, but not on the witness list, the DA, within the discretion of the judge, can usually get away with calling that witness at trial. The reasoning is the witness should not prejudice the defense because the witness was known all along. If the known witness gave a new statement that is materially different from the earlier statement then it may be a ground to exclude the witness.
Providing a list within the 30 days of trial the DA risks that other witnesses not known to the defense may be excluded. Many times I see the DA claim that he or she did not know about the witness even though the police officer or DA investigator did. Some judges, but not most, will exclude a witness of this type based on attributing the other law enforcement agency's conduct to the DA.
Game playing on the DA's part? It happens more than it should but not all prosecutors try to bias the playing field.
A surprise witness at the last minute may be allowed if it is clear the DA, with diligence could not have found the witness early. The defense however will be at least entitled to enough time to prepare for that witness, which may include investigation. If it looks like the defense needs a great deal of time and there is a jury sitting around waiting the judge will have to decide whether to exclude the witness or grant a continuance that will cause a mistrial. If there were a mistrial at the request of the defense it would not count as double jeopardy. If caused by the prosecution, it may be considered double jeopardy.
Every case is different. Specific facts of your case must be applied before relying on an answer to a general question. The answer given here is a general statement of the law on the issue that you presented in your question.
You need relax and trust your attorney. DAs play games but there are statutory and constitutional discovery laws and cases that limit "trial by surprise". If DA attempts to call unexpected witnesses judge will either exclude (or more likely) allow continuance to prepare for witness and get rebuttal witnesses, etc. leaving aside "Perry Mason" like dramatization, most witnesses are known and predictable by defense. Good luck
They must disclose who they plan to call. Otherwise the Judge might exclude them or sanction the prosecutor for a 1054 or Brady violation. Rebuttal witnesses, however, are the exception. They can only rebut what defense witnesses testified to. So a prosecutor could put on a witness in rebuttal that the defense did not know about. If a defense witness testified to a detail such as I was with the defendant at the time of the crime and the DA had a witness to say that the defense wit could not have been with the defendant at that time because they had proof they were elsewhere, that rebuttal witness could testify without the defense knowing before trial.
Penal Code Section 1054 requires that both parties give the opposing counsel a witness list 30 days before trial, or as soon as practicable. At times the DA finds a new witness, which must be disclosed immediately if within 30 days of trial.
Rebuttal witnesses do not have to be disclosed, if they are truly rebuttal and could not have been anticipated. The DA runs a risk that the court excludes a rebuttal witness (upon motion from defense) if they "sandbag," or wait until late to disclose witnesses.