My guess is that the Librarian instilled MC with a some forerunner DNA which caused him to be mentally linked to the other forerunners (ie Didact in this situation). Would make sense I suppose. --- Gamertag:SonowRaevius,psn:SonowRaevius Youtube:sonow666.
Personally I assumed that because the Librarian speeded up Chiefs evolution, he now has the ability of a telepath, if only to converse with Forerunners. Didact was thus speaking to chief telepathically not using any technology which Cortana could hack into and eavesdrop on.