As I was playtesting my Necro vs. Warlock, my Plague Zombie was burned and had 3 damage on it. I rolled the die and it killed the Plague Zombie. There was the opponent's mage and creature in that zone and it had rotted them. Since it's still during the Upkeep Phase, does the damage and Plague Master ability of the Necro work right then and there or does it take affect next Upkeep?

Curious on how that works. Thanks!