HCI has recently increased its interest in the domains of museums and gifting.The former is often oriented primarily towards the past, while the latter is often oriented towards the future, in terms of anticipating the receiver's reactions. Our article provides a sustained and well-evidenced new theoretical framework on the role of time-orientation on the design of forward-oriented (gifting) experiences in past-oriented (museum) settings. This Temporal Experience Design Framework develops from the analysis of two such studies, one smartphone app and one VR experience using passive haptics. Both interventions prompted the user to reflect on the past while planning a gift or donation for future consumption. We apply a novel combination of analyses to both projects using the lenses of conversational storytelling, performance, and human geography. Our analyses reveal the power of orienting users towards the past and the future -simultaneously -to enhance the present moment of a performative engagement. Our aim is to provide a conceptual framework that can help design researchers to identify, name, and understand how time-orientation can be used to enhance user and visitor experience. We also extrapolate design guidelines that we expect may be fruitful outside these contexts.