The reason is that you were entering into an airside/secure area when you exited the customs area. From the South Satellite, you could have gone upstairs to board NW, US and various other international flights, taken the automated bus to the B concourse, or take a shuttle bus from there to get to the D & C concourses - all airside. That's why you have to recheck checked bags to reclaim them again in the main terminal.
The Seattle satellites aren't very well organised in this regard. Other than for PIT, I am not aware of any airport where international arrivals do not exit from the customs hall to the landside/non-secure area.
[This message has been edited by terenz (edited 02-20-2002).]