Is it true that the burden of proof implies that the person making the allegation should provide evidence for it?

Yes, that is correct. The burden of proof is the responsibility placed on the person making an allegation or claim to provide evidence to support it. In legal contexts, the burden of proof is typically on the prosecution to prove the guilt of the defendant beyond a reasonable doubt. In other contexts, such as debates or discussions, the burden of proof may be on the person making a controversial claim to provide evidence or reasoning to support their position.