Ruzhan's Brand on killed enemies

Never really done any sort of minion / summoner build before but thought disciple looked fun.

With the way that Ruzhan's Brand is worded it's not clear to me if it ONLY explodes after a delay or detonated, or if it also explodes when the enemy it's on died, since it doesn't mention the enemy dying like Living Bomb does.

Just wondering if killing an enemy with the brand on it would be a "waste".