This was also the question I had while playing. I admit this makes sense, but where in the rules does it state that I should move the tokens?
Page 4 of the setup, tells you the top left is the unclaimed token area and the top of the study is the active/earned claim tokens. So moving it thereis implied with the raising of that experiment.
Also, even when the Study experiment is still on 1, is it still possible to get a temporary claim on a card?
Yes, read page 7, unclaimed compounds.