I would not fly to Madrid the same day as your overseas flight. You are not protected if your Seville flight is late arriving in Madrid, or cancelled. And I have seen complaints on Tripadvisor regarding cancelled flights at Seville. If you do choose to fly the same day, you need to allow 4-6 hours between the flights, which I would consider a waste of time. And even then it could go wrong.
Priscilla has offered some good suggestions. Travel back to Madrid the day before, late in the evening if you like. And take the train---it is actually faster than flying, by the time you add in travel time to the airport and necessary security time.
There are decent hotels within walking distance of Atocha station---we stayed at a 4* business hotel!for 90€ a few years back. We walked back to the station in the morning and caught the yellow airport bus. Quick and easy, and stress-free.