Passport Control

No, you will go through passport control at Amsterdam Schipol Airport. There is a divide between the sections of the airport with flights to/from non-Schengen destinations and Schengen destinations. You will get your passport checked there on your way to your next gate. Your luggage will be transferred automatically to Budapest and when you pick it up, you pass through Customs, which is normally just a matter of walking out the Nothing to Declare door.

I will add this usually does not take very long, but if you get to 30 minutes before your next flight, request to be moved up in the line. They have been doing this for as long as I can remember, which is the early 90's.

As Sam said, you do need to go through passport control. Usually it's pretty easy but depending on when you get there, it can get quite crowded and sometimes there are long lines.

If that happens, make sure that you let one of the employees who are walking around know that you have a very quick layover and they will get you into a special line for people who are leaving within the hour. They're usually pretty good about making an announcement to people and telling them that if you have a flight within a certain amount of time, to head over to this line. But just in case, find somebody and let them know.

Schiphol in general is a very easy airport to maneuver your way through so you shouldn't have any problem.

I’ll just add that you might look to see when the next KLM flight is to Budapest. They may do them every few hours but it may relieve some anxiety if you know what the rest of the day looks like, lol.

KLM has a few flights to Budapest each day. If your flight leaving San Francisco is departing late, you can see if the KLM ground staff at SFO can put you on the next available flight in order to take a bit of the pressure off at Schiphol. We have had this change done prior to leaving Vancouver for Europe when our connection has become too tight.

Are both flights on a single ticket?

What I see on the KLM site for SFO-AMS-BUD has a 2 hr 10 min layover in Amsterdam.

If two tickets and checked bags, I would say you are doomed. If no checked bags you are living on a razors edge.

@Joe32F, In May, it is 1 hr 10 min.

Sam
As OP didn't favor us with when he plans to travel, but I noted his one other post had to do with Christmas markets, so based my comments on a trip more near term than May.

Its been several years since I made a connection in AMS, but it wasnt an airport that I would want to make a 1:10 connection in. And now the OP has to mess with the EES thing too.

I think AMS is a very easy airport for connections. Everything is one terminal; you just book it to your gate -- the passport control will be along the path where it is requires and if your fight leaves in half an hour or less you get to bypass the line -- they list flights that can do this. The terminal is zoned into Schengen and non Schengen and there are guides on line so you willl have the picture of what you need to do.

It is huge so it is a long walk but it is well organized for transit. I would go on line and look at the transfer information. When I did it, there was a video of the entire route I needed to take so I knew what to do and it went easily/. I had a bit longer to transfer -- 90 minutes -- but if they have scheduled you on one ticket for this connection, it should be doable on one ticket.

I have flown through Amsterdam often, and have had a number of connection that were like yours, just over an hour, and always made it with time to spare to my gate.

Maybe some helpful information.

When you get out of the plane, you are just let into the international terminal, no maze of hallways to passport control. Look for signs to connecting flights, follow those. It helps to know your departure gate, as you walk you will see signs indicating groups of gates, since there are multiple passport control areas for connecting flights. It really does not matter which one you go to, but I usually go to the one directed. As you approach the passport control area, there will be a monitor, if your flight is listed, then you can go to the priority lane, otherwise just get in line, it moves quickly.