Season the turkey: Toss shredded turkey with soy sauce, sesame oil, and lime juice. Set aside.
Prepare the wrappers: Fill a shallow dish with warm water. Dip one rice paper wrapper for 5–8 seconds until pliable but not floppy. Lay on a clean surface or a clean dish towel.
Add fillings: Layer vermicelli noodles, turkey, carrots, cucumber, cabbage, mango, mint, and green onions across the lower third of the wrapper.
Seal the rolls: Fold bottom edge over filling, fold sides inward, then roll tightly upward.
Repeat with remaining wrappers.