No, if you double click the cards on the first turn, then they'll keep going back to the wrong position when inspecting them on the next turns. If you instead avoid inspecting those cards on the first turn, they'll go back to the proper position when you inspect them the next turn (and the rest of the battle).
what you said didn't happen for me. playing Arghan, i waited until round 3. same thing, Beast and Giant go back to the wrong slots, same as before. oh well, maybe next time.