I think this article is a little behind the times. Duffey's three highest-leverage appearances have all been in the month of June. Two successes, one fail IMO (whether or not the runs counted as earned). 21 batters faced in those 3 games, 12 outs recorded. Jury's out, I'd say, but it's not been stellar.
His OPS is better than league average, and for relievers I find that a simpler way to assess results than to pick through unearned runs and inherited runners and so forth. I guess the braintrust noticed too, and decided to start testing him a little more when it matters, about three weeks ago.
Has Duffey gotten a few high leverage appearances this month? Yes. But let's break down these appearances real quick.
The most recent one was the 17 inning Red Sox game. Literally all 8 of the pitchers in the Twins bullpen pitched in a high leverage situation in this game, and Duffey only got in after Rogers, May and Harper had already been used.
Another one was the Mariners game on June 12th, where the Twins had already turned to Morin, May and Parker in important spots before they went to Duffey. Also Rogers was unavailable due to his back issue.
The other high leverage spot was on June 7th against Detroit. A game in which both Rogers and May were unavailable due to high pitch counts in the previous two days. So the Twins had to turn to Morin, Harper, Duffey and Parker for high leverage innings in this game.
The rest of Duffey's outings have been in very low leverage spots when the Twins were down by a few runs, or had a huge lead.
To me it looks like Duffey has only been used in high leverage spots out of necessity, and not because the Twins actually wanted him pitching there.