Okay, but the rules reference I posted above clearly states that the controller of the creature decides the order of effects and event related to that creature.
Below the rule in the rulebook is the following example:
"Example: You control a Highland Unicorn with the Regenerate 2 trait
that has a Burn marker on it. Since the creature has a lot of damage on
it, the Burn effect could destroy it. You can choose to resolve the
Regenerate trait first or the Burn condition first."
I would assume that, following the above example, that if opponent had an enchantment, let's say ghoul rot, attached to the unicorn. Controller of the unicorn can again choose the order of damage and regeneration. Opponent has no say in this, because it is not his creature, even though he is controller of the ghoul rot. And the same would then go for drown.