The amulets Remille gave them were supposed to merely HIDE THEIR PRESENCE from the Darkspawn. While at the same time acting as a beacon for the Architect, so he knew EXACTLY where they are.
Duncan was protected not by the lack of his amulet, but because he stole a dagger from the First Enchanter's room - this dagger was created using Architect's magic, and thus made the person carrying it immune to the Amulet.
It is true, however, that the Amulet sped up the Taint in their bodies, as even Fiona, who was about half a year since her Joining started to show signs of The Calling, much like Wardens who were with the Order for 20-30 years (which is the regular lifetime from the Joining to the Calling, shorter for Wardens who are around during a Blight). King Maric was protected from the Amulet's speed up by the fact he was NOT a Warden.
Lastly, the only three survivors, Fiona, Maric and Duncan had respectively: The Taint removed completely; Not Tainted in the first place; Protected from bad effects of the Amulet.
Maric went on doing his King stuff.
Fiona was sent to Weisshaupt in the Anderfels to provide a detailed report, and act as a test subject (as the Wardens would obviously like to know HOW to remove the Taint) - eventually she was dismissed, as she says in Inquisition
Duncan became the 2IC of Wardens in Ferelden - keep in mind that he had some twenty years between The Calling and Origins to become the Warden-Commander, as Alistair is about 20 in Origins, and he was a new-born in the Epilogue of The Calling.