One hour might be a "legal connection" for Iberia, but it will be tight, at best. Madrid's Terminal 4 is massive—one of the biggest terminals in the world. You'll pull into a gate at the flanks of the non-Schengen satellite, walk towards the center to passport control, down three (or four) flights to the train, take the train to T4's main section, go up 3 (or 4) flights, through a full security process, and then walk out to your departure gate somewhere in the main terminal. And remember that gates close 10-15 minutes prior to scheduled departure.
Yes, if you missed the connection the airline would rebook you to the next flights that have space available, which may not be the next flight. To each their own, but I always prefer to make plans that don't have that level of stress built-in right off the bat.