If the flight from Cork is on time, you shouldn't have a problem. However, if the flight is delayed much at all, it's going to make your connection time tight. Airlines tend to book connections based on flights being on time, and when they're not, it's easy to miss a tight connection.
According to Wikipedia, AerLingus usually operates from Pier D (in hall 2) and Alitalia departs from Pier B (in hall 1). If you look at a map of the airport, you can get an idea of how far you'll need to transit:
http://www.nwa.com/travel/images/AMS2.gif
Depending on the gate assignment, it shouldn't be too far, because you're staying at one end of the airport. Last time I was there, I transitted D to E, and it took about 20 minutes, including immigration.
Dealing with immigration shouldn't be too much trouble. My husband is South Asian and they rarely spend more time with him than with me (US passport). If you're really in a rush, one thing I might suggest is tucking your boarding pass or something into your passport at the page with your current Schengen visa. That way it will be easier to locate, saving them the time of looking for it, especially if you have a large, full passport.
Worst case scenario, if something goes wrong and you do miss your flight, Alitalia has nearly half a dozen flights to Milan-Malpensa later in the day, so they may be able to rebook you on one of those. Not as close as Linate, but much closer than Schiphol!
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