In the past year, I have had about ten 60 minute connections in Madrid between T4 and T4S and vice versa. They have all worked out; most times relatively comfortably taking 30-40 minutes but a few have involved late arriving flights or long queues at passport control and then it has been stressful. A couple of times I have arrived at the departure gate with flight closed showing on the screens for my flight but the staff waiting for me and other connecting passengers. I now feel comfortable in booking the connection but I keep my hand baggage to a minimum to help me not have to wait for lifts etc.

As others have said you will go through passport control and a security/hand baggage check. There is also a decent walk as Madrid is a large airport and you have to get to and from the underground train connection between T4S and T4. There will no doubt be lots of other people also rushing about and worrying about connections! So the best advice I think I can offer is to hustle along as quickly as you can and research the airport layout in advance if you can.