All quite easy really,
The PM selects reverse as soon as main wheel touch down. The PF then continues or cancels reverse if directional control becomes an issue.
The introduction of this SOP caused a few initial problems when I was flying for Big Airways, (like nobody selected reverse at all !!!) but then everybody settled down to it.
Observing from the car park adjacent to 26L at LGW it was always the Big Airways planes that had reverse selected before the 'others'.
Leaving Big I flew for two other operators who both insisted the PF pulled reverse. (one of these a large West African carrier). Handling a landing in a xwind on a wet and poorly drained runway meant I was a couple of seconds late with reverse.