question about arriving in Amsterdam on the way to Rome

The general rule of thumb is that at your first stop in the Schengen Zone, if your final destination is in the Schengen Zone, you will proceed through Immigration (Passport Control) and then proceed to your connecting flight. Assuming both flights were made on the same itinerary, your bags (if any checked bags) will be checked through to Rome, so you only need to get yourself to your next gate. Someone else may have recent experience with Schipol Airport, but there is also an off chance that you may have to go through Security as well, or at least at some airports it seems you do. Very rarely, depending on the coding of the flight and the airport, you may not have to got through passport control, but don't count on it. If for whatever reason you made the two reservations independently (US Carrier then a budget flight) then an hour will not be anywhere near enough. If on the same itinerary, then usually the airline works to get you through in time. I have been escorted to my next flight, plane held. and of course you can always be put on the next flight. The airline is responsible for getting you there.

We were on a similar tight schedule before Christmas and missed our connecting flight. First the plane was about 15 mins late to the gate, second we were buried in the far back corner opposite the door which added another 20 mins or so to get off the plane. You go through immigrations and then security again for domestic flights plus a long walk. The lines were very long for both. There was a person controlling the lines and allowing passengers with short connections into the short line. Security was the same. It all helped but we still missed our connection by about 5 minutes. Try for a seat near the door so you can get off quickly, look for the person controlling the lines and take advantage, and walk quickly -- the Amsterdam airport is huge. You go through customs in Rome. Nothing unusual but it all takes time.

Other poster was correct, s/w your airline and see if you can get seats towards the exit so you can get off plane earlier. Also, you can usually find out what gate they will arrive in at Amsterdam and maybe find out which gate you will leave from for Rome. They do sometimes change gates but it is worth a shot. You can look up Schipol airport layout on their website and at least get an idea of where gates, etc. are as it is huge airport, maybe some of this will help.

We connect often through Schipol (AMS) and a 1-hour connection, having to go through immigration/passport control will be tight. Not sure what airline you're on (hopefully KLM out of AMS) but I'd certainly look at what my "next" flight options might be. In addition, even if you make the flight, your luggage may not make this narrow connection - so do take a change of clothes in your carry-on!

Schipol is a large airport. When my wife and I arrived there from Seattle, we were surprised we didn't get immediately herded into Passport Control. We just walked off the airplane into a gate area. And since Delta is not KLM, they get the gates that are waay out from the main area of the airport, so a lot of walking! I don't know if you need to go through Passport Control unless you need to retrieve some luggage and recheck it onto your plane to Rome. If you need to do that, then yes, you need to follow the signs to Baggage Claim, which will take you through Passport Control, and then down to the Baggage Claim area. When I arrived in Japan (Narita Airport) and had a connecting flight to Osaka, I didn't need to go through customs at Narita, instead I proceeded to board my next flight and went through customs in Osaka. But that was 25 years ago. I don't think 1 hour is enough time to do all this and check in to your new flight. Hopefully you aren't checking any luggage! If you aren't checking any luggage, you may be able to just proceed from your arriving flight directly to the gate for your new flight, and bypass Passport Control at Schipol. Boarding usually begins 50 minutes before departure, so by the time you get off the flight from Atlanta your flight to Rome will already be boarding. You might want to contact the connecting airline and see what will happen if you miss the flight to Rome. Hopefully they have another one you can take, or you'll be stranded at Schipol for a day.

Well, too late now (I guess you're there) but I just flew Detroit to Rome via Amsterdam. I did have to go through both passport control and security in Amsterdam even though it was just a layover. On the way back to the US I found that while passport control was as normal, they did security at the gate at Schipol. Once you were through security you were stuck at the gate - no stores, no restaurants. I don't fly much so this was a total suprise.