There is a question, that came up on the last tournament.

My opponent was playing Discombobulator on one of my creatures.
The question, that came up, who is now protected from the Ember steal.
I thought it was me, because my creature got the effect: "Your ember cannot be stolen". But my opponent said, it is his effect, and thought he is protected from Ember steal effects. As in, the "you" is still the owner of the upgrade card, and not the owner of the creature it is attached to.

It did not change anything at all, since i could not steal anything, and he just wanted the 1 Ember from playing it. But this question bothers me.

Discombobulator grants the constant ability to the creature that it is attached to, so if it is attached to your creature, then your Æmber cannot be stolen.

Note that an upgrade like Quadracorder does not grant the ability to the creature, so it would apply to the controller of the upgrade. Upgrades enter play under the control of the player who plays them.