Is the definition of anode and cathode failing?
entropid's answer is correct, but I'll try to express it differently. As Bard et al. state in Electrochemical Dictionary (1), the concept of anode and cathode is related only to the direction of electron flow: The anode is the electrode at which oxidation occurs (in an electrochemical cell) and electrons flow from electrolyte to electrode and the cathode is where reduction occurs and electrons flow from electrode to electrolyte. In a galvanic cell with a zinc anode, the electrons are flowing away from the interface in the electrode. Similarly, in a phototube, electrons emitted by the cathode are collected by the anode and again, electrons are moving away from the interface in the anode.

Where the electrons are actually coming from isn't important, just what direction they flow with respect to the electrode interface. Electrons moving from interface towards electrode = anode, electrons moving from electrode towards interface = cathode.

(1) Electrochemical Dictionary; Bard, A. J.; Inzelt, G.; Scholz, F., Eds.; Springer Berlin Heidelberg: Berlin, Heidelberg, 2008, pp 31.