Pat the chicken dry, then cover it evenly with the jerk paste and the juice from 1 lime in a mixing bowl. Cover the mixing bowl with plastic wrap and refrigerate overnight.
Preheat grill to High. This is the time to start your wooden skewers soaking in water so they don't burn on the grill. When the grill is hot and the skewers are good and soaked through, put the chicken on the skewers, with mango and bell pepper in between each piece of chicken.
Turn the grill heat down to Medium and place chicken skewers on the grill. You'll cook the skewers for about 8 minutes, turning once. While the chicken is cooking, grill the tomatoes cut-side down for about 3 minutes.
Remove skewers and tomatoes from heat and pull chicken and fruit off the skewers. Let them cool a little bit.
Toss the greens with the olive oil, then add the remaining lime juice, cucumber, cilantro, and onion. Finally, toss in the chicken, fruit, and grilled tomatoes.