Either crew member can call stop (although there are limited items which an FO is allowed to call stop for to aid ambiguity). PF retards the thrust levers to idle and PM selects max reverse. Once the engines are at forward idle and parking brake is set Captain takes control and roles are reversed to CM1 (who is effectively now PF) and CM2 (who runs ECAM, paper checklists) sounds complex but actually no big deal.
This is IMHO an astonishing method. I suspect, if the a/c goes off-road during an RTO, that the XAA's and insurance company will have some acerbic comments. It suggests that a low/medium experienced F/O is in charge of stopping & steering the a/c during a high speed RTO. Strong cross wind, short slippery limiting runway, auto brake disarms and max braking not applied, captain searching for the thrust reversers and is head down.
"I'm my defence, m'lud, I was only obeying SOP's. I know I am the captain and take final responsibility for the safety of the operation, but.............."