According to Vedanta, three states of consciousness are there --- jAgrat, svapna and sushupti. The Atman is known as viSva, taijasa and prAjna in these three states respectively.The turIya is the fourth which is different from the three. According to Paingala Upanishad there are five states - Waking, dream, deep sleep,swoon and death.
There is a forward movement from one state to another which involves the intermediary stage.
Thus from waking to dream , there is an intermediary stage. This in my humble view has to be construed as belonging to the previous State of consciousness. Thus the intermediary stage between waking and dream experience should be considered as waking state.. Similarly the intermediary stage between dream and deep sleep experience should be considered as dream state
According to SAstras, in the state of deep sleep, there is total ignorance about the existence of the objects except the awareness that "I Exist." While the experience during waking and dreaming states is different for different people, the deep sleep state is same for all. The witness "I" exists in all the three states.
Considering the position of SAstras on this topic, if the meeting of one's departed ancestor has happened in the intermediary stage just before svapna, it has to be construed as jAgrat state. If it has happened in the intermediary stage just before deep sleep, it has to be construed as svapna state.