Each character has the same stat array; the d6 just sets the order for that character.
For example: 3d6 are rolled six times resulting in: 17, 15, 11, 10, 10, 8. Each player will use this array.
For each 3d6 roll (17, 15, etc.) Umbran rolls a d6 where 1 equals strength, 2 equals dexterity...