Heat 1 tsp. oil in medium skillet over medium-high heat. Add onions, garlic, chipotle pepper, ½ tsp. Adobo and cumin; cook, stirring occasionally with wooden spoon, until onions are soft and translucent, about 7 minutes. Pour tamarind nectar into skillet; bring to boil. Lower heat to medium low; simmer, stirring occasionally, until nectar mixture begins to thicken slightly, about 5 minutes. Carefully blend tamarind mixture in blender until smooth, about 30 seconds. Transfer sauce to medium bowl; set aside until cool.
Heat grill or grill pan to medium-high heat. Thread chicken onto 4 pre-soaked wooden skewers. Drizzle remaining olive oil over chicken; rub to spread evenly. Season chicken with remaining Adobo. Add skewers to hot, greased grill grates. Cook, turning occasionally, until golden brown on all sides, about 6 minutes. Continue cooking, brushing chicken with reserved tamarind sauce and turning occasionally, until chicken is cooked through, about 10 minutes more.
To serve, transfer chicken skewers to platter; sprinkle with sliced scallions.