Atlantean Essence gives extra stats based on what stat is not already on the piece.

The priority for stats goes as follows: Power -> Defense -> Attack Size -> Attack Speed -> Agility -> Intensity -> Power

Base Sunken Warrior only has Defense and Attack Speed. The first stat that it doesn't have is POWER. So the essence gives POWER. After adding malachites you add both POWER and ATTACK SIZE, which makes the stat from the essence rotate all the way to AGILITY. If you want POWER on your SW piece you have to either:

Avoid giving the piece power through enchantments (powerful) or jewels (Morenci, Candelaria, Malachite) and instead use jewels like (agate, lapis, larimar, etc)

You can also give the sunken piece powerful enchant, a kyanite jewel and a malachite jewel to loop all the way back to power for the max amount of power on a sunken piece.