The aim of the present study was to examine how the organizational context of a non-profit organization (NPO) influences the motivation and work behaviors of volunteers. We hypothesized that the organizational context—operationalized by the motivational potential of the tasks, autonomy supportiveness of the supervisor, and value congruence between volunteer and NPO—can benefit or thwart self-determined motivation, which in turn predicts work engagement and organizational citizenship behaviors (OCB). In particular, the innovative aim of the study was to differentiate between general and organization-focused self-determined motivation (general and organization-focused SDM). Structural Equation Modeling revealed a distinction based on data from 2,222 volunteers: general SDM was related to the motivational potential of the task, whereas value congruence accounted for organization-focused SDM. Autonomy supportiveness of the supervisor similarly influenced both foci. Furthermore, general SDM enhanced work engagement, whereas OCB was solely linked to organization-focused SDM.