When mentally placing yourself in the past or future, different regions of the brain are active.
Past & Future: The left hippocampus and posterior visuospatial regions.
Future: The right hippocampus, right frontopolar cortex, and the left ventrolateral prefrontal cortex.
And when aligning future events with one's goals, the ventral medial prefrontal cortex and posterior cingulate cortex are active.
If there is some way to stimulate these respective regions and remove any sort of semblance of presence and self within the present, I feel it's reasonable to think it could be indistinguishable from time travel to the person who received this stimulation. This would qualify for your hallucination type of time travel. It would be literally indistinguishable.
There's a great paper on PubMed called Schizotypy and mental time travel. which summarises that "those scoring highly on positive schizotypy reported a greater sense of 'autonoetic awareness,' defined as a greater feeling of mental time travel and re-living/'pre-living' imagined events."
All you have to do is stimulate the right areas of the brain, through the drug or otherwise.