Q: How can I determine the exact position in global coordinates in my mass geometry during tracking and how can I convert it to coordinates local to the current volume ?

A: You need again to do it through the touchables (see also section 4.1.5 of the User's Guide for Application Developers), as follows:

      G4Step* aStep = ..;
      G4StepPoint* preStepPoint = aStep->GetPreStepPoint();
      G4TouchableHandle theTouchable = preStepPoint->GetTouchableHandle();
      G4ThreeVector worldPosition = preStepPoint->GetPosition();
      G4ThreeVector localPosition = theTouchable->GetHistory()->
                                    GetTopTransform().TransformPoint(worldPosition);
  
where worldPosition here stays for the position related to the world volume, while localPosition refers to the coordinates local to the volume where the particle is currently placed.