This summary is not the rule. The rule text controls.
If someone is on trial for murder and the prosecution proves that person actually committed the killing, the responsibility shifts to the defendant. At that point, the defendant must prove any facts that would lower the charge, or that would justify or excuse what happened.
This means the defendant cannot just sit back and claim self defense or say the killing was actually manslaughter. The defendant has to bring forward proof to support that claim. For example, if someone says they killed in self defense, they need to show evidence backing that up, rather than just denying guilt.
There is one exception to this rule. If the prosecution's own evidence already suggests the killing might only be manslaughter, or that the defendant had a valid excuse or justification, then the defendant does not carry this extra burden. In that situation, the prosecution's evidence has already raised the issue, so the defendant does not need to prove it separately.