For a rigify rig the fingers curl is controled by scaling S. This automaticaly rotates all finger bones at once.
I suggest you first:
don't use this setting, that could be confusing sometimes when you have to choose a control.
Use this one
then the rig should be like that:
If i want to move it no problem it works!!
and works still with fingers pressing G or R
If i want to move a finger i right click on control near the finger; this one it will change color (light blue) then G or R (let's use R in our example) and we'll have this situation
move now the mouse and the mesh will deform like you want; for example
Now the point is: i can't understand why this should not work for you. Please check all these thing
PS: after check all, remember to Save User preferences than quit blender and restart it.