If an item starting from common can reach Divine ( for example: Iron Boots, Nightmare etc.), you have to use Common Ascension Relics to get it to Divine, and for items starting from Rare rarity you have to use Rare Ascension Relics to get it to Divine ( for example: Malice Beam and Corrupt Light).
Same thing goes for Epic to Divine ( for example: Windigo, Zarkares, Nightfall etc.) you have to use Epic Ascension Relics. And same goes for Legendary (using Legendary Ascension Relics). (for example: Valiant Sniper, Magma Blast, etc.)
Also you can't use, for example, Rare Ascension Relics for items that start from Common ( like Nightmare). Same stuff for other rarities.
Hope this helps!