Heat oil in a Dutch oven or large pot over medium-high heat until shimmering. Add onions and garlic and cook, stirring occasionally, until onions have soften up, about 5 minutes. Add cumin and cook until fragrant, about 30 seconds. Add tomatoes, chipotle, and apple cider vinegar and stir to combine. Simmer for 5 minutes, season with salt and pepper. Remove from heat.
Transfer sauce to a blender and puree until smooth. Pour sauce back into Dutch oven over low-med heat, stir in chicken stock and shredded chicken into sauce, simmer until it thickens slightly, about 10 minutes. Remove from heat and adjust salt to taste.
Slice buns in half. Spoon tinga into the buns, garnish with red onion, and a dollop of sour cream. Top with a spoonful of sauce.