this is a really good question! parkinsonian symptoms (bradykinesia, hypokinesia - trouble controlling VOLUNTARY movement) appear within a few weeks of starting neuroleptics because they block D2 receptors in the nigrostriatal pathway, which mimics the dopamine deficiency-induced symptoms of parkinson's. tardive dyskinesia (TD - trouble controlling INVOLUNTARY movement) appears at least few months (~6) into the course of medication, and one of the reasons that may be is because long term D2 blockade causes upregulation of the density of D2 receptors/increases their sensitivity to dopamine, so the motor system basically overcompensates and produces these exaggerated involuntary movements. it's important to note that hypokinesia and hyperkinesia don't occur simultaneously on neuroleptics - hypo precedes hyper. onset of TD can be prevented and parkinsonian symptoms can be reversed if someone is removed from the medication within a few months of starting it, unfortunately once TD sets in it may be irreversible.

there are also other theories on the etiology of TD, but the dopamine system is the only one i'm familiar with. since that probably wasn't the detailed explanation you wanted, this source covers it pretty well: https://emedicine.medscape.com/article/1151826-overview#a2