It’s not a joint rotation or retargeting problem but a skin weighing problem.
To get the forearm to twist properly you need to blend the weighting through a chain starting at the shoulder. To see the needed effect place you right hand out in front of you palm down and rotate it until it’s palm up.
Notice how the forearm twists with the hand? This is what the twist bone is used for.
To fix it in your example you will need to balance the blend between the lower arm joint > lower arm twist > hand.