The handle of a cleaning rod spins in order to follow the twist of the bore. If your handle spins "from" the rod does that mean it spins off the rod? If so, that is a little problem. The handle rides on a bearing and should spin freely.
A chamber brush has no grooves to follow because it does not go past the chamber. It merely goes into the chamber and then out; therefore, it does not matter whether the handle rotates or not.