Dear Djdato;
As the Anode is “defind” as the electrod who “takes” the electrons out of the electrolyte, it has to be this way.
In the galvanic cell you are only watching the “outer” part of the electron flow, while in the electrolytic cell you “see” only the “inner” part of the electron flow.
But both need each other, or otherwise no electron flow can be realised.
(In physics current flows opposite to electrons.)
Good Luck!
ARGOS++