Cpt should keep one hand on the thrust levers,no matter who is PF,and he will perform the RTO.
If the cpt is PF ,the FO will call the failure (in simple,precise terms,i.e. eng failure,vibrations,oil pressure,etc..),the capt will call REJECT and perform the RTO.
If the FO is PF the cpt will call failure,like above ,then HE will decide also -REJECT-and will start the RTO.The FO will mantain control of the a/c (directional control) until positive control from the cpt who also has to say I have control.
No call for at or after V1.
All this must be as simple as possible as to not create any confusion among the crew.
this is also described in the NNM of the QRH
Brgds Alex