Just a point of terminology. There are tickets, and there are seat reservations. For some train systems, these can be bought separately. For Italo, when you buy your ticket, you get a seat reservation (as you say). However, there is no "reservation" all by itself for Italo - what you have are "tickets" with "seat reservations."
I mention this because if you refer to your ticket as your "train reservation," some may get confused (I did, and had to read your post twice). Just call it a ticket.
With your printed tickets, you just go to the station. As you have been told, for Italo trains you do not need to go through additional screening or security. You wait until your train departure track is posted, and go to that track. You may have to show your tickets to get onto the platform. On the train, the conductor will scan your ticket.
That's it.
For a large station, if it's your first time there, you will want to get there a bit early to use the toilet, buy a snack, and get your bearings. Once you know a station better, you can get there much closer to departure. As said above, they don't post tracks too early. I once saw a tourist in Prague nearly have a heart attack, because it was well over an hour before her train departure, and while the train was posted, the track wasn't. I tried to explain that this is how it works, and the track will be posted in plenty of time for her to get to the train (it was a small station with only four platforms), but she would not be comforted.