Q: I equip my opponent’s unit with Delayed Poison. When does that unit die?
A: When you equip a unit with an augment, that unit’s controller also becomes the controller of that augment. This means that “at the start of your next turn” will apply to the controller of the Delayed Poison, so the unit will be destroyed at the beginning of your opponent’s turn. (See cards that Equip – 184.108.40.206)