Rail Baron, my apologies, our airport is a complete mess right now. I've been flying out of here for eleven years and it's never been worse than right this minute.
If you arrived on a Horizon flight from Portland you came into the C Concourse and would not have needed to ride a train back to the main terminal. There is a van shuttle that takes Horizon passengers from the C Concourse over to NW in the South Satellite, but it's easy to miss. For future reference, it's on the right side as you're leaving the C Concourse opposite Gate C1. If you use that I don't know why you'd have to be rescreened once you got over there.
If you miss the shuttle, though, you do have to exit the secure zone, go downstairs to the S gate screening area, get screened again and wait for the underground train to take you over to the South Satellite.
If you came in on United Express from Portland rather than Horizon, you deplaned at the North Satellite and would indeed have had to ride the underground train back to the main terminal, exit the secure zone, hike the length of the terminal to the S gate screening area, get rescreened and catch another train to the South Satellite. It's incredibly poorly designed, frustrating and time-consuming.
If it's any consolation the locals are just as mad as you were...