In temporal interaction networks, vertices correspond to entities, which exchange data quantities (e.g., money, bytes, messages) over time. Tracking the origin of data that have reached a given vertex at any time can help data analysts to understand the reasons behind the accumulated quantity at the vertex or behind the interactions between entities. In this paper, we study data provenance in a temporal interaction network. We investigate alternative propagation models that may apply to different application scenarios. For each such model, we propose annotation mechanisms that track the origin of propagated data in the network and the routes of data quantities. Besides analyzing the space and time complexity of these mechanisms, we propose techniques that reduce their cost in practice, by either (i) limiting provenance tracking to a subset of vertices or groups of vertices, or (ii) tracking provenance only for quantities that were generated in the near past or limiting the provenance data in each vertex by a budget constraint. Our experimental evaluation on five real datasets shows that quantity propagation models based on generation time or receipt order scale well on large graphs; on the other hand, a model that propagates quantities proportionally has high space and time requirements and can benefit from the aforementioned cost reduction techniques.