Uptier Unique: Tiered Unique + Arcane Crystal + Rune (any) -> re-roll Tiered Unique as 1 tier higher.
Make sure you don't forget to add a rune when you use the above recipe, if you forget the rune it will uptier the base item but it won't upgrade the affixes.
Cube doesn't do a thing with the random rune in there. When one removes the rune the re-roll up a tier happens and I believe affixes go up as well.