You're quite correct, of course, that it would be for Parliament to pass whatever legislation is required to enter into or to bring a treaty into force. It is not uncommon in legislation that regulatory changes are required when a treaty is brought into force and that those are foreseen at the time the legislation is passed.
In answer to your question about whether parliamentarians get the final say on that, this regulation, like others under the Firearms Act, does require tabling in both houses of Parliament, and is therefore available for scrutiny by committees of both houses. That's a requirement of regulations made pursuant to the Firearms Act.