It's not a cooling off period. It's a last right to negotiation in favour of his current club.
This only happens when the contract is submitted to the NRL based on terms agreed by the player and the new club. Terms are agreed.
Does that bind the player to that contract if he does not accept his current clubs offer? That, I don't know.
Agree, though the system seems clunky and there's more to play out with various situations across different players and clubs to see the true impact of this new rule.