This is one of the two auras from items that can be used to improve champion pets, along with the Captain boot enchantment.
In game description: "Nearby allied minions deal 15% increased damage."
Contrary to the in-game description, Banner of Command does not increase a minion's total damage. Instead, it increases their attack damage or ability power stats. As such, Banner Of Command only increases the damage dealt by the minion's basic attacks and has no effect on other damaging effects the pet has (such as Tibber's aura).
Voidlings deal damage based on their AD and deal physical damage.
Gain a bonus 3 + (.75 × level) (+ 15% bonus AD) attack damage.
After 7 seconds, this bonus increases to 4.5 + (1.125 × level) (+ 22.5% bonus AD).
Every 100 bonus AD Malzahar has will grant his voidlings 115 attack damage, which increases to 122.5 after 7 seconds. At level 18 with 280 bonus attack damage, his voidlings will go from 390 attack damage (585 after 7 seconds) to 448.5 attack damage (672.75 after 7 seconds).