In a small saucepan, combine the fruit, honey, vinegar, chipotle, and adobo sauce. If the mixture seems dry, add 1 tablespoon water.
Bring to a boil, then reduce the heat and simmer, stirring occasionally.
As the mixture simmers, smash the berries against the side of the pan with a wooden spoon. Continue cooking until the berries have mostly disintegrated, about 10 minutes.
Pour the mixture through a strainer into a bowl. To extract as much liquid as possible, press the mixture firmly against the strainer and scrape the bottom of the strainer occasionally with a separate spoon. Discard the solids.
Preheat the grill.
Rub each tenderloin with about 1 tablespoon of olive oil, then season with salt and pepper.
Transfer to the grill and cook, turning a few times, until the turkey reaches an internal temperature of 165°F, about 20-25 minutes.
Place the turkey on a cutting board and let it rest for about 10 minutes.
Cut the turkey into thin slices and serve with the sauce.