Hello Frederic VE,
Yes, most activated carbons have an increase in initial pH for a few cycles. The reason for this initial increase is due to hydrogen (as H+) exchange. Some of the H+ from the activation process in activated carbon is exchanged with other cations, and eventually reacts with other anions (as the pH) decreases. The initial hydrogen exchange occurs with other cations, such as calcium that you mentioned. Some suppliers of activated carbon have treatments for lowering or preventing the initial pH increase.
I hope this explanation helps you out.
Best wishes,
Eugene