This is something that everyone encounters when they start transcribing, and it can make you want to tear your hair out. A picture is the wrong way round, you rotate it, so transcribe, save - and then see that it's back the way it was.
In the absence of any explanation and instructions from BG, the secret of getting the photos to stay rotated seems to be: rotate, WAIT 15-20 seconds, REFRESH the screen, then transcribe and save. It's the waiting and refreshing that seems to do the trick.
If after doing all that, the saved thumbnails are still the wrong way round, click on a thumbnail, and it will should right itself automatically. If it doesn't, try clearing your browser cache.
The best step-by-step instructions I've seen on getting your rotated pictures to stay rotated, and in particular, how to do it even after the images have already been transcribed, were written by Whitejaegar (Jim), and are here: