Do I do customs in Minneapolis? Layover times?

At your first entry point in the United States from Rome, you will go through passport control then on through customs. You will need to retrieve your luggage, follow connections for your next flight and drop your luggage for your next flight. If you are flying with the same airline and they booked your ticket with 1.15 hours in between, they usually allow what they think you will need.

MSP website says it takes about 30 min to clear customs. You have to go through customs at the first point of entry.
https://www.mspairport.com/about-msp/faqs.aspx#customs

I would say that 1 hour and 15 min is pretty tight considering the flight may get in late - probably doable but tight. You pretty much will have to scramble to meet the connection and hope your bags get transferred quickly. Most flights board at least a half hour prior to takeoff so that doesn't leave you much time to grab something to eat or relax in between the flights.

I wouldn't use a travel agent next time. It's very easy to book your own flight these days. Did you ask your travel agent if this connection is adequate based on their experience?

Hope for the best, prepare for the worst. Depending on how big an aircraft you are on, and how far back you are from the front, it can take 20-30 minutes just to get off the plane (independent of the airport). Depending on where your checked bags are (if you will have any) I have waited over an hour at the carousel for them to get to baggage claim, which you need to pick up before you can go through customs. So its always a gamble, no matter what airport.

I haven't connected at MSP but you will typically need to retrieve your checked baggage before the US customs then recheck to your final US destination after clearing customs. Just follow the line.

PS If you bought liquids at the Rome duty free shop, you will need to put the liquids (over 100 ml) into your checked baggage after customs and before rechecking you baggage.

As long as your flight is on one ticket, like it is in this case. You are protected. If there is a delay, the airline will rebook you. You'll go though passport control, then get your bags and clear customs.

Even if your bags are checked through to SLC, you still pick them up in customs.

After customs you will drop off your bags, go through security and go to the gate for your next flight.

If there is a delay, you may be greated by airline officials, or just need to use a ticket machine or wait in line for an agent where it's possible to recheck bags after customs. They would print you new boarding cards for alternate flights.

I always recommend not making important plans on the same day or day after you arrive from a transatlantic flight. While flights are usually uneventful, if there are delays, they can often be really long with the long distances involved. Especially in the summer when school is out and Europeans are on summer vacations.

Yes, you'll go through immigration and customs at MSP.
I think it's going to be very tight, unfortunately. MSP is a nice airport but it has some long concourses so it could be some distance between your arrival and departure points. You will have to hustle!

You will go through immigration and customs in Minneapolis. IMHO 1 hour and 15 minutes is not enough time to get through immigration then retrieve your bag from the carousel, get through the customs, sometimes they want to x-ray your bag or even open it and then to get to your gate. It would be enough just for change of planes.

As Nordheim said, if both flights are on one ticket (probably, since a travel agent booked it) any delays are the airline's problem. Just don't dawdle or make unnecessary stops. (Use the toilets on the plane about a half hour before landing time to avoid the last minute rush.)

We will be doing carry on so no baggage from the carousel. Also we are on the back end of the plane

Yes, I noticed several responses missed that you have carry on luggage only. My suggestion is to let your flight attendants know your predicament. They may be able to find you an available seat closer to the front and/or cue you up front to deplane first. It's worth a try.

Ditto to what everyone said. A couple years back I had this same experience, albeit different airports. I was flying from Nice, France, back to San Francisco with a plane change in Washington DC. The first segment was on a Lufthansa plane while the second segment was on a United plane, however, the entire trip was booked through United and on a United ticket. The layover time in DC was...(drum roll).... 50 MINUTES! If any of you have flown in/out of DC (Dulles airport), you know that not only are the international arrivals and domestic departures in two completely different buildings, but require a strange and cumbersome truck/bus like transport to get from one to the other, meaning, this is not some kind of sleek monorail type thing where you're quickly whisked away from one terminal to the next. The bus has to wait for everyone to board before moving. Needless to say, this was a ridiculously impossible connection time. We (and most of the other passengers) missed our connecting flight and after lining up for well over an hour at the United service desk, we were able to get on a later flight. Make sure you study the airport map for the airport where your layover is so you know how far the distance is between the gate you're arriving at and departing from. Do a sanity check to see if the time you have is enough just to walk/travel from one get to the next.

I agree with the others that is a tight connection. MSP is my home airport, and compared to other airports in the US, I tend to find that customs here is generally one of the better airports to go through, but obviously some days are better than others. MSP only has 1 main terminal and I've linked to the map below. Budget airlines like SWA and charters do flight out of a 2nd terminal but since a TA booked it I'm assuming you are on the same airline.

https://www.mspairport.com/images/directions/T1_quickmap_01_2016.aspx

We just returned from an overseas trip and went through Minneapolis. We were flying Delta and had a short time between the international flight's arrival and the domestic flight's departure. We also just had carry on luggage. We had no problem making the connecting flight. In fact, it was one of the easiest connections we've had.

Do you have Global Entry / TSA precheck? If not that is a way too short of a time IMO. Delta will definitely put you a on a later flight if miss your scheduled one.

The MSP airport uses machines where you put your passport on it, answer the questions, have your picture taken, and then bring the form and passport to the agent. The pictures look like your worse selfie! I find that what takes the most time is waiting to get off of the plane. Sometimes there isn't a gate available. But the flight attendants are usually helpful and if the flight is running late, have requested that the passengers with connecting flights be allowed to deplane first.

Just remember Delta will put you on the next flight with available space, not necessarily the next available flight.

I, too, fly thru SLC. I booked months ago on the LHR->SLC direct flight for Sept and they wound up cancelling that whole flight and booked me thru MSP to SLC with a 1h20m layover. I just didn't feel that was enough time and asked to be put on the later flight from MSP to SLC but was told it was full. I wound up choosing another day (so I could get the direct flight) which didn't matter much to my schedule.

I do now have Global Entry and would probably give a shorter transit thru MSP a try if I had to take that routing.

I have been thru there a couple of times and find it an easy airport but bigger than SLC in the amount of walking you have to do. I have also found that occasionally Delta will hold up their outbound flights to a hub if they know one of their big inbound flights is late.