It's actually perfectly fine for your opponent to have two of the same bird showing at once! The opponent's birds that are shown are not necessarily the ones they started off with. The birds shown simply reflects the order in which the birds were used. Let's say the opponent had two Terences. In this case they used Terence, as well as another other bird to fill up the destructometer. They then received another Terence and decided to use it straight away after receiving it. Thus both of the Terences would be shown at the same time, as that was the order in which the birds were used!