If you have a Sistarran Robes equiped to your mage and an Essence Drain attached to an opponent's creature, would Sistarran Robes activate when then opponent pays the Upkeep for the creature Essence Drain is attached to?

I would say yes because the opponent pays mana (for the upkeep) because of an effect you control (the essence drain card).

Sistarran Robes: "Once per round, when an opponent pays or loses mana because of an effect you control, you gain 1 mana."
Essence Drain: "This creature gains the Upkeep +2 trait.
Upkeep + X: "This object's controller pays X mana during each Upkeep Pahse or this object is destroyed."