There's a bug in your logic. Yes, if a new contract is proposed and a party declines the terms, there is no new contract. But that has no impact on the old contract.

So the old contract is still in effect, as it was not replaced by a new contract. So who terminated the old contract? That's the question here, and the conclusion seems to be that the employer is the one who then fired the employee, the employee did not quit by refusing the new contract.