i thought it also increases HP too
so if an eidolon gives 100 HP and 1000 atk matching the team's element, then the end result should be 110 HP and 1100 more atk
not sure if it's on nutaku myself.... haven't tested it out lately (i know it wasn't there months ago at least)
and if you have the weapon they like (someone said it was swords for Ares), then it doesn't matter where it is as long as it's on your grid, even for souls