Yes, I would also suggest the belt trick.
The tensioner CAN be affected by the A/C. The whole idea behind it is that over the years as the belt becomes permanently stretched longer and longer, it will maintain the proper grip around the pulleys. But with heavy loads, a belt can temporarily stretch too! It may return to its former shape for the most part or completely, but it can cause a bit of "fake" stretch.
One interesting experiment is to observe the tensioner while someone turns the steering wheel, or turns the A/C on. You might get a pretty noticeable movement in it. Even without this, you'll sometimes notice very slight up and down movements just as the engine idles.
Source: At a warehouse I worked at, some of the high-speed belts had pneumatic tensioners instead of fixed ones, you could really see the movement. Also in a ~400 long strands of chain fashioned in a loop with aluminum slats connecting them, when the drive was coming up to speed you could see a lot of slack in the catenary from load stretch until it evened out when the drive achieved speed.
Though I am confused about why it still happens after shutoff. How long after?
