A composite storage server employs a plurality of distributed storage sites including a mount site, a source copy site and one ore more copy target sites for executing a storage of volume data within the composite storage server. In operation, a deferred copy target site receives a communication of a source copy complete message from the mount site, the source copy complete message being indicative of the source copy site having a complete copy of the volume data, and detects a transition by the mount site of the host job from an active status to an inactive status subsequent to the communication of the source copy complete message from the mount site. Based on the inactive status of the host job, the deferred copy target site pulls the volume data from a peer distributed storage site having a complete copy of the volume data.