If you're not Spanish (and I'm guessing you're not), you'll first have to pass through customs/immigration and then possibly get your bags and re-check (yourself and your bags) into the counter for your Madrid-Sevilla domestic/national flight.
Is the brand new terminal for domestic or international flights? We boarded our flight in the international terminal, but then when we had the mechanical problems, they walked us down to the domestic/national terminal for lunch, to wait, and then we reboarded there.
From ticketing, you'll have to go through the security-check to/through the new, long terminal, they have several walking tracks (moving sidewalks/belts) to get you through faster.
Don't worry. I'm sure they'll make it all clear when you leave the plane.
Saludos, MadridMan
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