Slightly off topic, Roman Civilian, religious question

[Epictetus]

Apparently some of the religious magistrates were given houses owned by the state. Cassius Dio relates a clever move by Augustus when he assumed the title:

On the death of Lepidus he was appointed high priest… inasmuch as it was absolutely necessary that the high priest should live in a public residence, he made a part of his own house public property. The house of the rex sacrificulus, however, he gave to the Vestal Virgins, because it was separated merely by a wall from their apartments.

Cassius Dio, 54.27.2-3

I assume that it was "absolutely necessary that the high priest should live in a public residence" because of religious reasons. However, being given a residence could almost be considered a salary of sorts - it was a free place to live, after all.

Evidently the rather obscure rex sacrificulus also had a public house, at least during the Republic.

I don’t know about the flamen. I haven’t found anything to say one way or the other. One interesting point: after consecrated into office he was emancipated from the control of his father (or at least some were). Did he then leave the family home? If so, did he have to buy his own, or did the state give him one?