The PM operating the reversers on landing I thought was strange, though I’ve never worked to that SOP myself.
"Strange" is an understatement. It has the potential to be downright dangerous.
Edited for brevity Extract from Boeing 737 FCTM:
Landing rollout on a slippery runway with crosswind..as the airplane starts to weathervane into the wind, the reverse thrust side force component adds to the crosswind component and drifts the airplane to the downwind side of the runway...also high braking forces reduce the capability of the tires to corner. To correct back to centreline, release the brakes and reduce reverse thrust to reverse idle.
Releasing the brakes increases the tire-cornering capability and contributes to maintaining or regaining control directional control. Setting reverse idle reduces the reverse thrust side force component without the requirement to go through the full reverser actuation cycle. When directional control using rudder pedal steering and differential braking is regained, apply maximum braking and symmetrical reverse thrust to stop the airplane.
With one pilot on the controls and the other on reverse thrust can you just imagine the confusion as both pilots try to coordinate their respective duties as the aircraft slides sideways. The obvious solution is that whoever is doing the landing does the reverse thrust handling as well.