thus, everything was visually in the correct location
but logically the group was still in its old place

Yes, exactly :)

one needs to ensure that the update method calls self.setPos(...) somewhere

This should happen automatically, if your subclass is correct (every change passed to base class). Usually there's no need to call update() to make position changes.
If you move your custom item by e.g. mouse dragging the moveEvent is propagated to the base class QGraphicsItem or -Group which holds the position. Your position change was probably made only in your subclass, which paints your item at that position, but won't move it.

For the benefit of future archaeologists digging in this area, here are some additional clues:

• the update method of my subclass was changing the position of the group's individual elements,
• but not the position of the group itself
• thus, everything was visually in the correct location
• but logically the group was still in its old place

Therefore, one needs to ensure that the update method calls self.setPos(...) somewhere.

Show your subclass.
I bet, you forgot to pass the new position to its base class, so that from scene's point of view, the item is still at its old position, which triggers the tooltip there.