There seems to be evidence, at least from lucid dreams, that the experience is in real time because communication is possible with dreamers (I find this mindblowing). Some report that they hear the signals as coming from objects in the dream (a radio, say). www.sciencedirect.com/science/arti...
Real-time dialogue between experimenters and dreamers during REM sleep
Dreams take us to a different reality, a hallucinatory world that feels as real as any waking experience. These often-bizarre episodes are emblematic …
sciencedirect.com