This technical note addresses the distributed time-varying formation-containment (FC) control problem for heterogeneous general linear multi-agent systems (MASs: the virtual leader, multi-leaders and followers) based on the output regulation framework from an observer viewpoint under the directed topology which contains a spanning tree. All agents can have different dynamics and different state dimensions. A new format of time-varying formation (TVF) shape is proposed. The multi-leaders are required to achieve the TVF with tracking the virtual leader whose output is only available to a subset of them, and only need to send the information of their designed observers and TVF shapes to their neighboring followers. A new class of distributed adaptive observer-based controllers is designed with the mild assumption that both leaders and followers are introspective (i.e., agents have knowledge of their own outputs). Compared with the existing works, one main contribution is that the controllers are fully distributed with the proposition of TVF shapes. The simulation to multi-vehicle systems is also provided to verify the effectiveness of theoretical results.