We did this tour last September and loved it!
We flew into Madrid and immediately took the high-speed train to Zaragoza for two nights. The high-speed train ticket includes a local train ticket (free) within a four hour window. We just asked directions from an agent on how to get from the airport to the high-speed station. Zaragoza is a lovely, walkable town just right for getting over jet-lag, and much cheaper than Barcelona. This could be a one-night stop.
We then took the high-speed train into Barcelona for two nights prior to the tour starting. This gave us time to see the sights the tour doesn't cover (Park Guell, Casa Bolta, Casa Mila, and we took a day trip to Girona.) We emailed the hotel in Barcelona and requested two nights additional stay, letting them know we were on the RS tour starting on the specific date (tours often overlap in hotels). We've done this on all our RS tours and they've always kept us in the same room. Makes it easier for them and us.
When the tour was over, we took the high-speed back to Madrid, stopping for the day in Cordoba to visit Mezquita-Catredal de Cordoba. We took a later high-speed train into Madrid for an additional two nights, again to see the sights the tour did not cover that we didn't have time for while the tour was in Madrid.
This was the first time we flew in and out of the same city. It just worked for this tour and our timing. Normally, we would arrive a day or two early to get over jet lag, staying at the RS. While it's tempting to fly out right after breakfast on the last day, it's nice to take the time to relax and be in the country almost as a local, without the tour! For the Spain tour, you'll probably find much better flight options out of Madrid than out of Sevilla.
All train tickets were booked separately. We had downloaded the Renfe app and all our train tickets were in our Apple wallet-it couldn't be easier.
Tips:
Instead of ordering Sangria (too sweet with added sugar), try Tinto de Verano instead. It's a mix of red wine and lemon soda water. Very tasty!
If you do arrive into Barcelona early enough for a day trip, the easiest choices are Monserrat or Girona. We chose not to go to Monserrat because we've been to Meteora in Greece and were looking for a city day trip.