Tardive Dyskinesia actually falls under the EPS (extrapyramidal symptoms) syndrome which may well include dystonia, parkinsonism etc.
Such EPS syndrome (especially physical movement disorders, including Hemifacial Spasms triggered by bodily chemical imbalances) in turn is caused by disturbances to the dopamine receptors (one of the main neurotransmitters) in the nervous system which is normally induced by most of the AAP's (atypical antipsychotics).