Ah yes, I see how the wording "start of play" could be interpreted... Still, I wonder if the Immortal is meant to always have 3 Interruptions with his Schemes. Otherwise, quickly abandoning the first 2 Schemes to gain 2 more later without any of the Interruptions feels cheap... Same problem with completing a Scheme. Why would the new Schemes not come with their own Interruptions.
Personally, I've always interpreted "start of play" as being a synonym for "start of session". Don't worry, you won"t be stuck with 4 Interruptions now. you can just pick the missing two and assign them wherever you want (keeping your old enemy, and perhaps having Poitevin reacting to your snooping around in his business).
When the rules or their wording are ambiguous, I try to fall back on the spirit of the game, and in US, there is no such thing as a free lunch...