Greg matches it on his turn and then it loses its reinforcements before the player can play his match /swap, meaning you DON’T get the extra turn.
When the player matches the support, the extra swap is given and the reinforcement is lost after the swap (greg gets no extra swap)
When reinforcing the support with extra cast cards, Greg gets an extra turn, then the reinforcements are removed BEFORE the layer can make his match, thus no extra turn.
Also in the third case, the support also loses ALL shields, without taking the newly cast versions into account (it should at least revert to 3 shield, but honestly it should be all the shield added by casting)
FWIW Thousand-Year Storm has had this same problem since forever (goes down to 1 shield instead of 4 when it loses all its reinforcements), so I wouldn’t hold my breath for a fix for this part.