When I (the Inflicter) inflict a Morale Test to one of my opponent's (the Target) units, who's deck do I draw cards from, mine or theirs? in a few games last weekend played using the tournament rules, we defaulted to the x-wing rules of using the damage deck of The Target. Did we do this right?

Per the tournament rules, each player provides their own Morale Deck which is not shared with your opponent (TR p. 4 under Player Materials; p. 8 under Step 7 of Game Setup). The Tournament Reference does not indicate who's deck The Inflicter draws cards from.
The Rules Reference (neither the original nor the one updated on 23rd August) makes no distinction on who's deck to draw from, presumably because it was written for using only a single deck. It only indicates that The Inflicter draws cards from the Morale Deck.

As I type this out, I think I have determined that we did it wrong. Given that The Inflicter draws the cards (RR 53.1), in the card text, "you" refers to The Inflicter (RR 53.5), and that Players do not share a morale deck (TR p. 8 Step 7), it would seem that The Inflicter draws from their own deck, as drawing from The Target's could be considered shearing. With causing fear, doubt, and confusion amongst my opponent's units being the antithesis of caring, I should not be sharing their deck.

Is my logic sound on this, or does a player suffer moral cards from their own deck?

You draw from your own morale deck. The attacker is the one who performs the test, so you use the attackers deck.

8 hours ago, Tvayumat said:

You draw from your own morale deck. The attacker is the one who performs the test, so you use the attackers deck.

Strange, but ultimately irrelevant as long as it is consistent. Stops cards from getting mixed up by passing cards.

3 hours ago, Darthain said:

Strange, but ultimately irrelevant as long as it is consistent. Stops cards from getting mixed up by passing cards.

Given what we know of Uthuk mechanics so far, it's not unreasonable to assume they may have some morale deck manipulation that makes this quite relevant.