Under the Julio-Claudians, Judaea was administered by an Imperial praefectus (prefect). That means that the Emperors personally appointed a representative governor, a military man, to run the territory. Technically, Judaea was an administrative sub-department of the province of Syria, which was also an "Imperial" province. In the principate, the Emperor "personally governed" most of the provinces which held legions or were otherwise considered problematic in some way. These were governed through his personal agents, called legates. On balance, the "quiet" provinces were deemed "Senatorial" and were run by senatorial governors, nominally distributed by the Senate. There was nothing particularly special about Judaea's government in the 1st century CE, and certainly nothing so unusual as to be a source of a "feeling of oppression." There were many provinces under Imperial prefects, and every single province of the Empire was governed by somebody, be it a prefect or a senatorial representative.

I wrote about Judaea's complicated road to becoming a Roman territory over here.

Following up now that I have more time: I have read more of the Aberbach(s) book and they have some compelling discussion about all this. I'm still not sold on all of it, but without a shadow of a doubt they should be listened to over me, any day of the week! My initial take was very much clouded by how you framed your question, which deals with basic Roman governing mechanisms in the late Republic and early Principate. In that regard, Imperial procurators were no different in Judaea than anywhere else, except that Judaea was in this odd limbo between sub-section of administrative district (Syria) and its own province (Judaea would, eventually, be turned into Roman provinces). I also don't much like their implication that procurators in Judaea were somehow worse than anywhere else. But yeah. Interesting book.