I have had the same problem - Shared Photo Streams (evidently) do not update dynamically. There is also no button to force an update in the photo app either.
On your iDevice by going into Settings > Photos & Camera and switching off "Shared Photo Streams". Go into your Photo app and check that they have been removed.
Now go back into the same Settings sub-menu and re-enable "Shared Photo Streams". Back in the Photo app, you will see the shared stream update with the correct photos.
I have the exact same problem with any shared photo streams I create on my iPhone - they do not appear on my iPad unless I do the above. The same goes for iPhoto/Aperture on my Mac.