From what I understand, "Full" equals what the creature's initial Atk was at time of casting and "Current" would be it's modified Atk, so morningstar would be right in that it should be reflected under "Current."
I don't know how big of a change the programing or algorithms would need to make this work, but from a little bit of testing the popup reflects any immediate change to the creature's Atk. So it seems the program is capable of recognzing changes to the creature and thus the algorithm or programing would need a simple table to draw it's modified adrenaline information from and insert it into the creature's Current Atk as a "Atk + X + Y" format.