Cervical spinal cord injury (SCI) can significantly impair an individual's hand functionality due to the disruption of nerve signals from the brain to the upper extremity. Robotic assistive hand exoskeletons have been proposed as a potential technology to facilitate improved patient rehabilitation outcomes, but few exoskeleton studies utilize standardized hand function tests and questionnaires to produce quantitative data regarding exoskeleton performance. This work presents the human subject case study evaluation of the FLEXotendon Glove-III, a 5 degree-of-freedom voice-controlled, tendon-driven soft robotic assistive hand exoskeleton for individuals with SCI. The exoskeleton system was evaluated in a case study with two individuals with SCI through two standardized hand function tests namely, the Jebsen-Taylor Hand Function Test and the Toronto Rehabilitation Institute Hand Function Test and three questionnaires (Capabilities of Upper Extremities Questionnaire, Orthotics Prosthetics Users Survey, Quebec User Evaluation of Satisfaction with Assistive Technology). Minor design changes were made to the exoskeleton: integrated fingertip force sensors to sense excessive grasp force, a quick connect system to expedite the exoskeleton glove swapping process between users, compact tendon tension sensors to measure tendon force for admittance control, and a redesigned smartphone app to encompass all aspects of exoskeleton use.