As a light cleric, I added an amulet of Devotion +1 and my spell save DC correctly adjusted on the spells page to 16, but my channel divinity feature still shows the DC is 15.

There's no official magic item called "Amulet of Devotion". So either this is homebrew or you meant "Amulet of the Devout"

If homebrew: check with the person who created it. 

If you meant Amulet of the Devout: the snippets/description is not updated because there is no {{insert Char's Spell Save Here}} coding for use in such. So, where your channel divinity is described it "builds" the save dc based on your spellcasting ability and cannot factor any other bonuses or features from other sources. Each such feature is a self-contained thing. This is a limitation of how features are organised and coded. The spell save DC is correctly updated in the Spell Save DC bit under spells on the character sheet. Since you know the channel divinity is based on your spell save DC, you should always look here for the most updated "spell save DC" for your character.