If the lasts few seasons of Serie A have proved anything the whole "a spent EPL player should be fine in a slower league like Serie A" notion is false. Evra doesn't count because he wasn't done IMO.
Looking at Miranda and Melo, I don't think it's an EPL thing with Mancini. It's more the case with Thohir than Mancini imo.
Mancini so far has shown his approach to the squad building relies significantly on players with big experience, "leaders", players who could be captains like Melo, Miranda, Vidic, Yaya Toure, Pirlo all fit that profile of an experienced leader with international rep and Ivanovic is similar, as a player with CL experience, as Chelsea's vice-captain etc.
I think both him and Vidic are physically and mentally drained athletes though. I would rather see Inter rely more on inventive coaching approach and creating distinctive style than just throwing experience at the problems waiting for us next season, like hopefully mid-week CL games.