If you're flying next month then I'm assuming you're on AA718, PHL-FCO.

I was almost positive that you'd be arriving in T3, but I just checked to be sure. And on AA.com and another flight tracking website it is incorrectly showing T5 as the arrival terminal - so that's probably where you got the bad info. But T5 is a terminal only set up for departures if flying directly to the US or Israel.

But then I tried another tracking site, and see today's flight showing arrival at T3:
http://www.flightstats.com/go/Flight...ate=2016-12-22

Of course this doesn't address the question of whether there'll be a TIM store/or kiosk there.

As of right now, ADR has yet to update their shopping map since last May when this was posted. You'll see in that link my post quoted in the post from pcharles, with the link to the stores in T3 Arrivals. I had seen then as I do now, that there's a TIM store in T3 Arrivals, but apparently that wasn't the case as noted by pcharles.

Sorry I'm not of more help, I'm anxious to hear a current report too. Good luck!