Add soy sauce, garlic, lime juice, vegetable oil, cumin, paprika, and oregano to a blender; blend until smooth. Pour into a gallon-sized resealable plastic bag. Add chicken thighs, coat with marinade, squeeze out excess air, seal the bag. Marinate in the refrigerator for 8 hours.

Add jalapeños, cilantro, mayonnaise, lime juice, olive oil, garlic, salt, and pepper to a blender; pulse until smooth. Transfer sauce to a bowl; cover and refrigerate until ready to serve.

Preheat an outdoor grill for medium-high heat and lightly oil the grate.

Remove chicken thighs from marinade and shake off excess. Discard bag and remaining marinade.

Cook chicken thighs on the preheated grill for 7 minutes; flip and grill 7 minutes more. Transfer to a serving dish; drizzle jalapeño sauce over chicken.