The ruling makes it very clear that core constitutional powers have conclusive and preclusive (absolute) immunity.
Other official acts have presumptive immunity.
In all cases, the motive is above question. If Trump has a fight with Melania, he can order the CIA to rendition and disappear her. He doesn't even need to claim that she's a spy. It can never be questioned in court. He can then pardon everyone involved, so even the underlings face no court.
In all cases, the official acts are explicitly not admissible as evidence. Using the example above, the District of Columbia can try to prosecute for murder, but is unable to introduce the fact of the order as evidence. If Trump receives a bribe, the official act that he undertook at the briber's behest is similarly inadmissible.