IANAL, but there are two types of immunity in criminal cases: “use” and “transactional”.
“Use” immunity allows (forces) you to answer questions in a criminal proceeding, and the prosecution cannot use your statements against you. However, if they can corroborate the facts of your testimony some other way, they can still prosecute you for the crime about which you testified.
“Transactional” immunity prohibits prosecution for the crime under any circumstances.
You are correct.