No, I don't (personally) believe all previous actions of a user should become "Moderator actions" (capitol 'M') once they gain that diamond ♦.
From 1-reputation upward, everyone on this site is earning increasing abilities to perform various "moderator actions." The whole site is based on community self-moderation. But when a moderator earns that diamond ♦, they explicitly become deputized with a few additional abilities not afforded anyone else (let's call them "official" actions, for lack of a better word).
You wouldn't want to say that all actions performed before and up to that point become ex post facto "official moderator actions." At the time those actions were performed, those users were not bound by the Moderator Agreement, nor were they privy to the information and abilities the officially-appointed moderator have. Those actions were not, by definition, official.
In that same vein, any official actions taken by a moderator♦ should not suddenly become un-official, should they relinquish their position.
As for handling these cases, it may be an oversight… a bug… or just one of those pedantic, edge cases not worth devoting the resources to right now. That's a discussion for another day.