No, Diamond Spray's Damage Doesn't Overcome DR X/Magic
The word magic there is nonmechanically descriptive; diamond spray's damage overcomes DR as if it were adamantine and cold iron. If the damage were meant to overcome DR X/magic, the spell would instead say
These magical slivers are treated as adamantine, cold iron, and magic for the purpose of overcoming damage reduction.
Or, maybe, like mythic chord of shards, it would say the spell "bypasses all damage reduction."
More on Pathfinder Damage Reduction
While it says here that "[s]pells, spell-like abilities, and energy attacks (even non-magical fire) ignore damage reduction," the FAQ clarifies by answering this question:
How does DR interact with magical effects that deal bludgeoning, piercing, or slashing damage?
Although the definition of Damage Reduction says "The creature takes normal damage from energy attacks (even non-magical ones), spells, spell-like abilities, and supernatural abilities," that's actually just referring to damage that isn't specifically called out as being of a particular type, such as fire damage or piercing damage. ... However, if a magical attack specifically mentions that it deals bludgeoning, piercing, or slashing damage, DR affects that damage normally, as if it were from a physical weapon.
Thus, if the spell diamond spray did not say the damage was slashing damage, it would automatically overcome DR as it's a spell. But because diamond spray specifies slashing damage then specifies adamantine and cold iron, diamond spray doesn't also overcome DR X/magic unless stated. The normal physical weapon, in this case, is treated as just adamantine and cold iron. Which is sad.