Heat a grill to medium-high, about 400°F. Rub pork with oil, garlic, rosemary, 1/2 teaspoon salt and pepper.
Toss apple and celery with mayonnaise, vinegar, sugar and remaining salt. Refrigerate while the pork cooks.
Grill the whole tenderloin with the lid closed, turning every 5 minutes, for 18 to 25 minutes until its thickest part reaches 145°F. Move to a cooler area if the outside browns before the center is ready.
Rest pork for 8 minutes, then cut across the grain into 1/2-inch medallions. Toast the cut bun faces on the grill for about 30 seconds.
Drain any collected liquid from the slaw. Divide warm pork and slaw among the buns, close and serve one sandwich per person immediately.